Physical Science Practice Questions — Armed Services Vocational Aptitude Battery (ASVAB) — Page 5

Question 81Question →

Complete the statement by providing the correct numerical coefficient and reaction classification for the chemical equation shown.

Fill in the blanks below

In the industrial synthesis of ammonia, the balanced chemical equation is $\text{N}_2 + \text{H}_2 \rightarrow 2\text{NH}_3$, and because multiple reactants combine into one compound, it is classified as a reaction.

Show answer & explanation

Answer

The missing coefficient is 3 (or three) and the reaction type is synthesis (or combination).

To balance the equation according to the law of conservation of mass, the 6 hydrogen atoms in

2\text{NH}_3

require a coefficient of 3 for diatomic

\text{H}_2

(

3 \times 2 = 6

). A chemical process where two or more substances combine into a single compound is classified as a synthesis (or combination) reaction.

Step-by-Step Solution

1

Count the total number of nitrogen and hydrogen atoms in the product molecules.

Two ammonia molecules (

2\text{NH}_3

) contain

2 \times 1 = 2

nitrogen atoms and

2 \times 3 = 6

hydrogen atoms.

The law of conservation of mass dictates that the number of atoms of each element on the reactant side must equal the number of atoms on the product side.

2

Determine the coefficient needed for diatomic hydrogen gas (

\text{H}_2

) on the reactant side.

Dividing the required 6 hydrogen atoms by the 2 atoms per

\text{H}_2

molecule yields a coefficient of 3.

Three molecules of

\text{H}_2

supply exactly 6 hydrogen atoms (

3 \times 2 = 6

), completely balancing the equation.

3

Classify the reaction based on the relationship between reactants and products.

Two distinct elemental reactants (

\text{N}_2

and

\text{H}_2

) combine chemically to produce a single product compound (

\text{NH}_3

).

Reactions that follow the general form

A + B \rightarrow AB

are defined as synthesis or combination reactions.

Key Concept

Balancing chemical equations via conservation of mass and identifying synthesis reactions

Estimated Time:1m 0s

Question 82Question →

In laboratory science, matter is characterized by distinct physical, chemical, intensive, and extensive behaviors. Match each classification of matter or property on the left with its corresponding laboratory example on the right.

Click a left item, then click its matching right item

Show answer & explanation

Answer

Intensive property correctly pairs with the boiling point of pure ethanol; Extensive property pairs with the total heat capacity of a ten-liter water sample; Chemical property pairs with the tendency of metallic iron to oxidize; Physical change pairs with the dissolution of crystalline table sugar into distilled water.

The correct pairings accurately reflect foundational physical science definitions: intensive properties (boiling point) are independent of system mass; extensive properties (total heat capacity) depend directly on the amount of matter; chemical properties (oxidation potential) govern reaction behavior; and physical changes (dissolution) preserve molecular structure.

Step-by-Step Solution

1

Differentiate intensive from extensive physical properties.

Intensive properties (such as boiling point) are invariant with sample mass, whereas extensive properties (such as total heat capacity) scale directly with quantity.

This establishes the fundamental distinction between intrinsic substance characteristics and bulk quantity-dependent measurements.

2

Evaluate the chemical property descriptor.

The tendency of iron to oxidize describes a reactivity characteristic that involves forming new chemical bonds.

Chemical properties can only be observed or measured by attempting to change the chemical identity of the substance.

3

Analyze the dissolution process.

Dissolving sucrose in water is a reversible physical transformation where molecular composition remains intact.

Since no chemical bonds within the sucrose molecules are created or destroyed, the process is classified as a physical change.

Key Concept

Classification of Matter: Intensive vs. Extensive Properties, Chemical Properties, and Physical Transformations

Estimated Time:1m 30s

Question 83Question →

In an acid-base neutralization reaction, aqueous hydrochloric acid ( $\text{HCl}$ ) mixes with aqueous sodium hydroxide ( $\text{NaOH}$ ) to produce table salt ( $\text{NaCl}$ ) and one neutral compound. What is the chemical formula of the missing product in the balanced reaction below?

Fill in the blanks below

\text{HCl} + \text{NaOH} \rightarrow \text{NaCl} +

Show answer & explanation

Answer

Water (

H_2O

)

In a neutralization reaction between an acid and a base, hydrogen ions (

H^+

) from the acid combine with hydroxide ions (

OH^-

) from the base to produce water (

H_2O

). The remaining sodium (

Na^+

) and chloride (

Cl^-

) ions form the salt sodium chloride (

NaCl

). Therefore, the missing product that balances the equation is

H_2O

.

Step-by-Step Solution

1

Identify the characteristic reaction type and components.

Hydrochloric acid (

HCl

) is an acid and sodium hydroxide (

NaOH

) is a base, reacting in a classic neutralization reaction.

An acid and a base neutralize each other to produce a salt (

NaCl

) and water.

2

Apply the law of conservation of mass to balance the atoms.

The reactants contain 2 hydrogen (

H

) atoms, 1 chlorine (

Cl

) atom, 1 sodium (

Na

) atom, and 1 oxygen (

O

) atom. Subtracting the sodium and chlorine in

NaCl

leaves 2 hydrogen atoms and 1 oxygen atom, which combine to form

H_2O

.

Atoms cannot be created or destroyed in a chemical reaction; all reactant atoms must appear in the products.

Key Concept

Acid-Base Neutralization and Law of Conservation of Mass

Estimated Time:45s

Question 84Question →

Match each physical property of matter on the left with its corresponding definition on the right.

Click a left item, then click its matching right item

Show answer & explanation

Answer

Malleability matches the ability to be hammered into thin sheets; Ductility matches the ability to be drawn into thin wires; Viscosity matches a fluid's resistance to flow; Density matches mass per unit volume.

Each physical property corresponds to a distinct observable behavior of matter: malleability allows flattening into sheets, ductility allows stretching into wires, viscosity measures resistance to liquid flow, and density expresses mass per unit volume.

Step-by-Step Solution

1

Identify the definitions for solid mechanical properties.

Malleability corresponds to shaping into sheets under pressure, and ductility corresponds to drawing into wires under tension.

Both are intensive physical properties describing deformation of solids without altering chemical composition.

2

Identify the definitions for fluid and volumetric properties.

Viscosity corresponds to fluid flow resistance, and density corresponds to the mass-to-volume ratio.

Viscosity governs fluid dynamics, whereas density describes how tightly packed mass is in a given space.

Key Concept

Characteristic physical properties of matter

Estimated Time:45s

Question 85Question →

Match each fundamental physical law of mechanics to the statement that correctly describes it.

Click a left item, then click its matching right item

Show answer & explanation

Answer

Newton's First Law pairs with the principle that an object maintains constant velocity unless acted on by an external net force; Newton's Second Law pairs with acceleration being proportional to net force and inversely proportional to mass (

F = ma

); Newton's Third Law pairs with equal and opposite action-reaction forces; Newton's Law of Universal Gravitation pairs with mutual mass-dependent attraction that weakens with distance squared.

Each mechanics law corresponds to its standard scientific definition: the First Law defines inertia (constant velocity without net force), the Second Law establishes the relationship between force, mass, and acceleration (

F = ma

), the Third Law describes equal and opposite interaction forces between bodies, and the Law of Universal Gravitation defines mutual mass attraction.

Step-by-Step Solution

1

Identify the principle governing motion when the net force is zero.

This describes inertia, which is Newton's First Law.

An object resists changes to its velocity when no net force acts on it.

2

Identify the formula and relationship linking net force, mass, and acceleration.

This corresponds to

F = ma

, which is Newton's Second Law.

Acceleration is produced when an unbalanced net force acts upon a given mass.

3

Identify the law governing force interactions between two distinct objects.

This corresponds to action-reaction pairs, which is Newton's Third Law.

Forces always act simultaneously in opposite directions on interacting bodies.

4

Identify the law describing mutual attraction between any two masses across space.

This corresponds to Newton's Law of Universal Gravitation.

Gravitational pull depends directly on the product of masses and inversely on distance squared.

Key Concept

Newton's Laws of Motion and Gravitation

Estimated Time:45s

Question 86Question →

An isotope of a neutral atom has a mass number of $31$ and contains $16$ neutrons in its nucleus. If this atom gains $3$ electrons to form a stable anion, what is the total number of subatomic particles (protons, neutrons, and electrons) in the resulting ion?

43

46

49

64

Show answer & explanation

Answer: $49$

Answer

The total number of subatomic particles in the resulting ion is

49

.

The atomic number is found by subtracting neutrons from the mass number (

31 - 16 = 15

protons). A neutral atom has

15

electrons, and gaining

3

electrons increases the electron count to

18

. Adding

15

protons,

16

neutrons, and

18

electrons gives a total of

49

subatomic particles.

Step-by-Step Solution

1

Determine the number of protons in the atom.

15

protons

The atomic number equals the mass number minus the number of neutrons:

31 - 16 = 15

.

2

Determine the number of electrons in the resulting anion.

18

electrons

A neutral atom has equal numbers of protons and electrons (

15

). Gaining

3

electrons yields

15 + 3 = 18

electrons.

3

Sum all subatomic particles (protons, neutrons, and electrons) in the ion.

15 + 16 + 18 = 49

The total particle count is the sum of

15

protons,

16

neutrons, and

18

electrons.

Key Concept

Calculating subatomic particle totals in ions using mass number and charge

Estimated Time:1m 30s

Question 87Question →

An automotive technician performs several actions on a piece of iron: cutting it to size, polishing its surface, heating it to bend it into shape, and leaving an unpainted scrap outside where it eventually forms reddish-brown rust. Which of these actions results in a chemical change?

Cutting the iron to a smaller size

Rusting after being exposed to outside air

Heating the iron until it bends

Polishing the surface to make it smooth and shiny

Show answer & explanation

Answer: Rusting after being exposed to outside air

Answer

Rusting after being exposed to outside air

Rusting is a chemical change because iron atoms react with oxygen in the atmosphere to create an entirely new compound, iron oxide.

Step-by-Step Solution

1

Define the difference between physical and chemical changes.

A physical change alters form, shape, or appearance without changing the underlying chemical identity. A chemical change produces one or more new substances with different chemical properties.

Understanding the fundamental criteria distinguishes changes in state/shape from chemical reactions.

2

Evaluate cutting, polishing, and heating/bending.

These actions modify only the size, surface texture, and shape of the iron, while the substance remains pure iron (

Fe

).

Changes in dimensions and mechanical deformation do not alter chemical bonds.

3

Evaluate the process of rusting.

Iron exposed to moisture and oxygen undergoes oxidation to form iron(III) oxide (

Fe_2O_3

), a completely new substance.

The creation of a new compound with distinct chemical properties defines a chemical change.

Key Concept

Physical versus Chemical Changes in Matter

Question 88Question →

A double-walled cryogenic storage container is engineered to maintain liquid nitrogen at extremely low temperatures by minimizing heat gain from the surrounding environment. Which of the following correctly pairs a structural feature of the container with the primary heat transfer mechanism it is designed to inhibit?

The evacuated vacuum space between the double walls primarily minimizes heat gain caused by infrared radiation.

The narrow, low-conductivity structural neck suspending the inner chamber primarily minimizes heat gain caused by fluid convection.

The silvered, mirror-like surface lining the walls primarily minimizes heat gain caused by thermal radiation.

The sealed, airtight exterior lid primarily minimizes heat gain caused by direct solid conduction through open air.

Show answer & explanation

Answer: The silvered, mirror-like surface lining the walls primarily minimizes heat gain caused by thermal radiation.

Answer

The silvered, mirror-like surface lining the walls primarily minimizes heat gain caused by thermal radiation.

Thermal radiation transfers energy through electromagnetic infrared waves and does not require particles or a material medium. Highly polished, silvered surfaces reflect these electromagnetic waves away from the inner chamber, significantly reducing radiative heat gain.

Step-by-Step Solution

1

Analyze the physical requirements of the three fundamental heat transfer mechanisms.

Conduction transfers kinetic energy through direct contact of particles in solids, convection transfers heat through the bulk movement of fluids (liquids or gases), and radiation transfers energy via electromagnetic waves without requiring any physical medium.

Understanding whether each transfer mechanism depends on matter is necessary to evaluate the function of each insulating barrier.

2

Examine how each specific component of the cryogenic container operates.

The evacuated space between the walls eliminates particles, blocking conduction and convection; the narrow composite neck reduces cross-sectional contact area, reducing solid conduction; the reflective silver lining reflects infrared electromagnetic waves.

Matching structural components to their physical principles reveals which pairing is scientifically valid.

3

Evaluate the pairing of the reflective lining with thermal radiation.

Because thermal radiation travels across the vacuum gap as electromagnetic waves, highly polished reflective surfaces are required to reflect these waves away from the cold storage chamber.

This confirms that the silvered surface specifically targets and mitigates radiative heat transfer.

Key Concept

Thermal Heat Transfer Mechanisms (Conduction, Convection, and Radiation)

Estimated Time:1m 15s

Question 89Question →

In an industrial chemical synthesis process, methane gas ( $\text{CH}_4$ ) reacts with high-temperature steam ( $\text{H}_2\text{O}$ ) to yield carbon monoxide ( $\text{CO}$ ) and hydrogen gas ( $\text{H}_2$ ) according to the following chemical equation:

\text{CH}_4 + \text{H}_2\text{O} \rightarrow \text{CO} + \underline{\quad ? \quad}\text{H}_2

What numerical coefficient must be placed in front of $\text{H}_2$ to balance the equation?

2

6

3

4

Show answer & explanation

Answer: 3

Answer

The numerical coefficient that balances the equation is 3.

The reactant side has a total of 6 hydrogen atoms: 4 from methane (

\text{CH}_4

) and 2 from steam (

\text{H}_2\text{O}

). Since molecular hydrogen gas is diatomic (

\text{H}_2

), a coefficient of 3 provides

3 \times 2 = 6

hydrogen atoms, successfully satisfying the Law of Conservation of Mass while leaving carbon and oxygen balanced at 1 atom each on both sides.

Step-by-Step Solution

1

Tally the number of each type of atom on the reactant side of the equation.

Reactants: 1 Carbon atom (from

\text{CH}_4

), 6 Hydrogen atoms (4 from

\text{CH}_4

plus 2 from

\text{H}_2\text{O}

), and 1 Oxygen atom (from

\text{H}_2\text{O}

).

According to the Law of Conservation of Mass, atoms cannot be created or destroyed, so total reactant atoms must equal total product atoms.

2

Tally the fixed atoms on the product side.

Products: 1 Carbon atom (in

\text{CO}

) and 1 Oxygen atom (in

\text{CO}

). Carbon and oxygen are already balanced (1 of each on both sides).

Identifies which elements are already balanced so attention can be directed to the unbalanced element.

3

Determine the required coefficient for diatomic hydrogen (

\text{H}_2

) to balance hydrogen.

To supply 6 hydrogen atoms using diatomic

\text{H}_2

molecules:

6 \div 2 = 3

.

Multiplying the coefficient 3 by the subscript 2 yields 6 hydrogen atoms, balancing the equation.

Key Concept

Balancing Chemical Equations and Conservation of Mass

Estimated Time:1m 0s

Question 90Question →

When methane gas ( $\text{CH}_4$ ) burns in the presence of oxygen gas ( $\text{O}_2$ ), it reacts to produce carbon dioxide ( $\text{CO}_2$ ) and water vapor ( $\text{H}_2\text{O}$ ). Which of the following statements correctly describes what happens to the atoms during this chemical reaction?

The molecules change their physical state without breaking or forming any chemical bonds.

The existing atoms break their original bonds and rearrange to form new chemical compounds.

The reactant atoms are destroyed during combustion and replaced by newly created product atoms.

The individual carbon and hydrogen atoms change their atomic numbers into different elements.

Show answer & explanation

Answer: The existing atoms break their original bonds and rearrange to form new chemical compounds.

Answer

The existing atoms break their original bonds and rearrange to form new chemical compounds.

In a chemical reaction, the original chemical bonds between reactant atoms break, and the atoms rearrange to form new bonds and produce distinct substances without creating or destroying any atoms.

Step-by-Step Solution

1

Identify the nature of the process described in the prompt.

The combustion of methane with oxygen is a chemical reaction that generates new substances (

\text{CO}_2

and

\text{H}_2\text{O}

).

A chemical reaction involves a change in chemical identity and composition, unlike a simple phase change.

2

Apply the principles of atomic theory and the Law of Conservation of Mass to the reaction.

The total number and identity of each atom remain constant, but the chemical bonds holding them together break and reform into new molecular structures.

Chemical reactions involve the rearrangement of valence electrons and chemical bonds between atoms, not the destruction or elemental transformation of atoms.

Key Concept

During a chemical reaction, existing chemical bonds are broken and atoms rearrange into new combinations to form different chemical compounds while conserving all atoms.

Estimated Time:45s

Question 91Question →

Read the chemical reaction scenario below and fill in the blanks with the correct numbers or terms.

Fill in the blanks below

During the complete combustion of butane (

C_4H_{10}

), the hydrocarbon reacts with oxygen gas (

O_2

) to produce carbon dioxide (

CO_2

) and water vapor (

H_2O

). When this chemical equation is balanced using the smallest possible whole numbers, the coefficient for oxygen (

O_2

) is and the sum of all coefficients in the balanced equation is . Furthermore, because this process releases net thermal energy to its surroundings, it is thermodynamically classified as an reaction.

Show answer & explanation

Answer

The balanced coefficient for oxygen is 13, the sum of all coefficients is 33, and the reaction is exothermic.

Balancing the complete combustion of butane requires compensating for an odd number of oxygen atoms on the product side by doubling all coefficients. This transforms the intermediate equation (

C_4H_{10} + 6.5O_2 \rightarrow 4CO_2 + 5H_2O

) into the proper whole-number equation (

2C_4H_{10} + 13O_2 \rightarrow 8CO_2 + 10H_2O

). The resulting oxygen coefficient is 13, and the total sum of coefficients is 2 + 13 + 8 + 10 = 33. Because the combustion process releases net thermal energy, it is classified as an exothermic reaction.

Step-by-Step Solution

1

Write the unbalanced skeletal equation for the combustion reaction.

C_4H_{10} + O_2 \rightarrow CO_2 + H_2O

Establishes the chemical formulas for all reactants and products before applying the law of conservation of mass.

2

Balance the carbon (C) and hydrogen (H) atoms first.

C_4H_{10} + O_2 \rightarrow 4CO_2 + 5H_2O

There are 4 carbons and 10 hydrogens in a butane molecule, requiring 4 molecules of carbon dioxide and 5 molecules of water to balance those elements.

3

Count the oxygen (O) atoms on the product side to determine the required oxygen on the reactant side.

Products have

(4 \times 2) + (5 \times 1) = 13

oxygen atoms. The reactants need

\frac{13}{2}

O_2

molecules.

Oxygen appears in only one reactant but multiple products, making it most efficient to balance last.

4

Multiply the entire equation by 2 to achieve the smallest whole-number coefficients.

2C_4H_{10} + 13O_2 \rightarrow 8CO_2 + 10H_2O

Standard chemical equations require the lowest possible whole-number coefficients, eliminating the fractional 6.5.

5

Identify the coefficient for oxygen and calculate the total sum of all coefficients.

Oxygen coefficient = 13. Sum =

2 + 13 + 8 + 10 = 33

.

This directly answers the first two blanks of the prompt based on the fully balanced equation.

6

Classify the reaction type based on its thermal energy transfer.

Exothermic.

Combustion reactions release heat energy into their surroundings, which is the definition of an exothermic process.

Key Concept

Advanced Stoichiometry and Thermochemistry

Question 92Question →

A sealed, hollow cylinder made of solid metal (density $= 6.0 \text{ g/cm}^3$ ) is placed in a liquid solvent (density $= 1.5 \text{ g/cm}^3$ ). The cylinder achieves neutral buoyancy, meaning it floats completely submerged without sinking or rising. If the total outer volume of the cylinder is $400 \text{ cm}^3$ , what is the volume of the hollow cavity inside the cylinder in $\text{cm}^3$ ?

Show answer & explanation

Answer: 300

Answer

300

For the cylinder to be neutrally buoyant, its total mass divided by its total volume must equal the fluid's density of

1.5 \text{ g/cm}^3

. With a total volume of

400 \text{ cm}^3

, the cylinder's total mass is

600 \text{ g}

. Since the entire mass comes from the metal shell, dividing this

600 \text{ g}

by the metal's true density (

6.0 \text{ g/cm}^3

) reveals that the actual metal occupies

100 \text{ cm}^3

. The remaining volume (

400 - 100

) must be the

300 \text{ cm}^3

hollow cavity.

Step-by-Step Solution

1

Determine the average density required for neutral buoyancy.

Average density =

1.5 \text{ g/cm}^3

An object that floats completely submerged (neutrally buoyant) must have an overall density exactly equal to the fluid it displaces.

2

Calculate the total mass of the cylinder.

Total mass =

600 \text{ g}

Mass equals the overall average density multiplied by total volume (

1.5 \times 400

).

3

Calculate the volume occupied by the solid metal itself.

Metal volume =

100 \text{ cm}^3

The solid metal volume equals the total mass divided by the solid metal's density (

600 / 6.0

). The hollow cavity contributes essentially zero mass.

4

Calculate the volume of the hollow cavity.

Cavity volume =

300 \text{ cm}^3

The cavity volume is the total outer volume minus the volume of the solid metal (

400 - 100

).

Key Concept

Density, extensive/intensive properties, and buoyancy of composite objects

Question 93Question →

A delivery van travels along a circular entrance ramp at a constant speed of $25\text{ mph}$ . Why is the vehicle considered to be accelerating even though the speedometer reading remains unchanged?

The van's weight decreases as gravitational pull weakens around the curve.

The speedometer records distance in miles rather than standard metric units.

The direction of travel is constantly changing, which alters the vehicle's velocity.

Speed is a vector quantity that automatically increases whenever an object turns.

Show answer & explanation

Answer: The direction of travel is constantly changing, which alters the vehicle's velocity.

Answer

The direction of travel is constantly changing, which alters the vehicle's velocity.

Acceleration is defined in physics as the rate of change of velocity over time. Because velocity is a vector quantity consisting of both speed and direction, an object traveling in a circle is continuously changing its direction. This continuous change in direction means the velocity vector is changing, which produces acceleration directed toward the center of the turn.

Step-by-Step Solution

1

Define the relationship between speed, velocity, and acceleration

Speed is a scalar quantity (magnitude only), whereas velocity is a vector quantity (both magnitude and direction). Acceleration (

a

) is the rate of change of velocity:

a = \frac{\Delta v}{\Delta t}

.

Determining whether an object is accelerating requires evaluating its velocity vector rather than just its scalar speed.

2

Analyze the motion of the vehicle on a curved path

Although the magnitude of the velocity (speed) is steady at

25\text{ mph}

, the direction of travel continuously turns along the curve.

A change in the direction of a vector constitutes a change in velocity.

3

Conclude whether acceleration occurs

Because velocity changes continuously with direction, the vehicle undergoes centripetal acceleration directed toward the center of the curve.

Any non-zero change in velocity over time confirms acceleration.

Key Concept

Velocity is a vector quantity comprising both magnitude and direction; thus, changing direction at constant speed results in acceleration.

Estimated Time:45s

Question 94Question →

Match each thermodynamic principle or heat transfer mechanism with the real-world scenario where it serves as the primary mode of thermal energy exchange.

Click a left item, then click its matching right item

Show answer & explanation

Answer

Direct kinetic energy transfer via collisions matches copper heat sink dissipation (conduction); bulk fluid displacement driven by density differences matches coastal sea breezes (convection); electromagnetic emission across empty space matches solar atmospheric warming (radiation); and isothermal phase-change energy absorption matches evaporative sweat cooling (latent heat).

Each thermodynamic mechanism is accurately paired with its primary real-world application: conduction governs kinetic transport through solid copper, convection governs atmospheric buoyancy circulation cells, radiation governs electromagnetic transfer across the vacuum of space, and latent heat governs the isothermal phase change of evaporating sweat.

Step-by-Step Solution

1

Identify the fundamental heat transfer mechanism described in each item on the left.

The left descriptions represent thermal conduction, natural convection, thermal radiation, and latent heat of vaporization, respectively.

Categorizing each physical description by its formal thermodynamic definition clarifies the governing laws of energy transport.

2

Analyze each scenario on the right to identify the dominant thermodynamic mechanism in operation.

The copper baseplate operates via solid conduction, coastal breezes operate via fluid convection, solar warming operates via radiative wave transport through a vacuum, and sweat evaporation operates via latent heat absorption.

Matching real-world physical systems to their underlying thermal transfer modes isolates the correct pairings.

3

Pair the theoretical definitions with their corresponding empirical physical scenarios.

Conduction pairs with the copper baseplate; convection pairs with coastal breeze circulation; radiation pairs with solar warming across space; latent heat pairs with sweat evaporation.

Ensures every description is paired unambiguously with its sole physical manifestation.

Key Concept

Distinguishing between microscopic conduction, macroscopic buoyant convection, electromagnetic radiation, and latent heat phase transitions in physical systems.

Estimated Time:1m 30s

Question 95Question →

A divalent metal cation ( $M^{2+}$ ) contains $18$ electrons. In the nucleus of this isotope, the number of neutrons is $4$ greater than the number of protons. What is the mass number of this isotope?

Show answer & explanation

Answer: 44

Answer

The mass number of this isotope is

44

.

A neutral atom that forms a divalent cation (

M^{2+}

) loses

2

electrons. Since the cation has

18

electrons, the neutral atom has

20

electrons and therefore

20

protons. The isotope has

4

more neutrons than protons, giving

20 + 4 = 24

neutrons. The mass number is the sum of protons and neutrons:

20 + 24 = 44

.

Step-by-Step Solution

1

Determine the atomic number (number of protons) from the cation's charge and electron configuration.

Protons =

20

A divalent cation (

M^{2+}

) has lost

2

electrons relative to its neutral state. The neutral atom therefore has

18 + 2 = 20

electrons and, correspondingly,

20

protons.

2

Calculate the total number of neutrons in the nucleus.

Neutrons =

24

The problem specifies that the number of neutrons exceeds the number of protons by

4

, giving

20 + 4 = 24

neutrons.

3

Sum the protons and neutrons to obtain the mass number (

A

).

Mass number =

44

The mass number of an isotope is defined as the total number of nucleons (protons plus neutrons):

20 + 24 = 44

.

Key Concept

Calculation of atomic number and mass number from ionic charge and subatomic particle relationships.

Estimated Time:1m 30s

Question 96Question →

Match each primary mechanism of heat transfer to the everyday scenario that best exemplifies it.

Click a left item, then click its matching right item

Show answer & explanation

Answer

Conduction matches the metal spoon heating up in hot soup; Convection matches warm air rising toward the ceiling while cool air sinks; Radiation matches feeling the warmth of sunlight on your skin through a window.

Thermal energy transfer operates through three fundamental pathways. Conduction occurs via direct physical contact where kinetic energy passes between neighboring particles, perfectly illustrated by the solid metal spoon heating up. Convection occurs in fluids (gases and liquids) as temperature variations cause density changes, producing convective currents where warmer, less dense air rises toward the ceiling. Radiation transfers heat via electromagnetic waves that travel across space independently of physical particle movement, as observed when sunlight warms the skin.

Step-by-Step Solution

1

Identify the physical state and mechanism for the first item (Conduction).

Conduction requires direct atomic or molecular contact within a solid or stationary material. The metal spoon in direct contact with hot soup represents this process.

Solids, especially metallic conductors, transfer heat along a temperature gradient via particle vibration and free electron movement.

2

Identify the physical state and mechanism for the second item (Convection).

Convection involves the macroscopic flow of fluids (liquids or gases). Air expanding, becoming less dense, and rising sets up a natural convection loop.

Temperature changes alter fluid density, generating buoyant upward forces for warm fluid and downward settling of cooler fluid.

3

Identify the physical state and mechanism for the third item (Radiation).

Radiation involves electromagnetic waves capable of traveling through a vacuum or transparent media like glass. Sunlight warming skin is radiant energy transfer.

Thermal radiation does not rely on matter-to-matter contact or circulating fluid streams to transport energy.

Key Concept

Distinct mechanisms of thermal energy transfer: conduction (direct contact), convection (fluid movement), and radiation (electromagnetic waves).

Estimated Time:45s

Question 97Question →

A technician inspects a solid metal component with a mass of $108\text{ g}$ and a volume of $12\text{ cm}^3$ . What is the density of the component in grams per cubic centimeter ( $\text{g/cm}^3$ )?

Show answer & explanation

Answer: 9

Answer

9 g/cm^3

Density measures the amount of mass contained per unit volume of a substance. Dividing the component's mass of

108\text{ g}

by its volume of

12\text{ cm}^3

gives a density of

9\text{ g/cm}^3

.

Step-by-Step Solution

1

Identify the given physical quantities from the problem statement

Mass (

m

) =

108\text{ g}

, Volume (

V

) =

12\text{ cm}^3

Density is a fundamental physical property defined as mass per unit volume.

2

Calculate the density using the formula

\text{Density} = \frac{\text{Mass}}{\text{Volume}}

\text{Density} = \frac{108\text{ g}}{12\text{ cm}^3} = 9\text{ g/cm}^3

Dividing the total mass of the object by its volume determines the mass contained in each cubic centimeter.

Key Concept

Density as a characteristic physical property of matter relating mass and volume

Estimated Time:45s

Question 98Question →

Four electric hoists in a maintenance facility lift cargo vertically at constant speeds. Arrange the hoists in order of their average mechanical power output, from lowest power to highest power.

Drag items to arrange them in the correct order

Show answer & explanation

Answer

The correct sequence from lowest to highest mechanical power is the hoist delivering

400\text{ W}

(

500\text{ N} \times 4\text{ m} / 5\text{ s}

), followed by the hoist delivering

500\text{ W}

(

250\text{ N} \times 10\text{ m} / 5\text{ s}

), then the hoist delivering

600\text{ W}

(

300\text{ N} \times 6\text{ m} / 3\text{ s}

), and ending with the hoist delivering

800\text{ W}

(

800\text{ N} \times 3\text{ m} / 3\text{ s}

).

Mechanical power equals the rate of doing work (

P = \frac{F \times d}{t}

). Computing the power output yields

400\text{ W}

for the

500\text{ N}

load over

4\text{ m}

in

5\text{ s}

,

500\text{ W}

for the

250\text{ N}

load over

10\text{ m}

in

5\text{ s}

,

600\text{ W}

for the

300\text{ N}

load over

6\text{ m}

in

3\text{ s}

, and

800\text{ W}

for the

800\text{ N}

load over

3\text{ m}

in

3\text{ s}

. This produces the ascending sequence

400\text{ W} \rightarrow 500\text{ W} \rightarrow 600\text{ W} \rightarrow 800\text{ W}

.

Step-by-Step Solution

1

Recall the formula for mechanical power in terms of force, distance, and time.

P = \frac{W}{t} = \frac{F \times d}{t}

where power (

P

) is in Watts (

\text{W}

), force (

F

) in Newtons (

\text{N}

), distance (

d

) in meters (

\text{m}

), and time (

t

) in seconds (

\text{s}

).

Power measures the rate at which work is performed.

2

Calculate the power output for each hoist.

First hoist:

(300\text{ N} \times 6\text{ m}) / 3\text{ s} = 1800\text{ J} / 3\text{ s} = 600\text{ W}

. Second hoist:

(500\text{ N} \times 4\text{ m}) / 5\text{ s} = 2000\text{ J} / 5\text{ s} = 400\text{ W}

. Third hoist:

(800\text{ N} \times 3\text{ m}) / 3\text{ s} = 2400\text{ J} / 3\text{ s} = 800\text{ W}

. Fourth hoist:

(250\text{ N} \times 10\text{ m}) / 5\text{ s} = 2500\text{ J} / 5\text{ s} = 500\text{ W}

.

Determines the exact numerical power for all four mechanical scenarios.

3

Arrange the resulting power values in ascending order.

400\text{ W} < 500\text{ W} < 600\text{ W} < 800\text{ W}

.

Satisfies the requirement to order from lowest power to highest power.

Key Concept

Power is the rate of doing work, defined as work divided by time (

P = \frac{W}{t} = \frac{F \times d}{t}

), and is measured in Watts.

Estimated Time:1m 15s

Question 99Question →

A motorized winch pulls a cable, accelerating a load from rest ( $0\text{ m/s}$ ) to a final velocity of $18\text{ m/s}$ in $6\text{ seconds}$ at a constant rate. What is the acceleration of the load in meters per second squared ( $\text{m/s}^2$ )?

Show answer & explanation

Answer: 3

Answer

The acceleration of the load is

3\text{ m/s}^2

.

Acceleration is calculated by dividing the total change in velocity by the elapsed time (

a = \frac{\Delta v}{t}

). Because the load accelerates uniformly from

0\text{ m/s}

to

18\text{ m/s}

over

6\text{ s}

, the acceleration is

\frac{18\text{ m/s} - 0\text{ m/s}}{6\text{ s}} = 3\text{ m/s}^2

.

Step-by-Step Solution

1

Identify the initial velocity, final velocity, and elapsed time from the given problem.

v_i = 0\text{ m/s}

,

v_f = 18\text{ m/s}

, and

t = 6\text{ s}

These parameters are required to calculate uniform linear acceleration.

2

Set up the acceleration formula:

a = \frac{\Delta v}{t} = \frac{v_f - v_i}{t}

.

a = \frac{18 - 0}{6}

Acceleration represents the rate of change of velocity with respect to time.

3

Perform the division to compute the numerical value.

a = 3\text{ m/s}^2

Dividing

18\text{ m/s}

by

6\text{ s}

yields

3\text{ m/s}^2

.

Key Concept

Linear acceleration is defined as the change in velocity divided by the time interval over which the change occurs (

a = \frac{\Delta v}{t}

).

Estimated Time:45s

Question 100Question →

Two solid samples of equal mass, Substance A and Substance B, are heated in separate insulated containers at the exact same constant rate. During the heating process, Substance A exhibits a much steeper rate of temperature increase prior to melting, but requires three times as much time to fully melt at its melting point compared to Substance B. Which of the following conclusions correctly compares the thermal properties of Substance A to Substance B?

Substance A has a higher specific heat capacity and a lower latent heat of fusion than Substance B.

Substance A has a lower specific heat capacity and a higher latent heat of fusion than Substance B.

Substance A has a higher specific heat capacity and a higher latent heat of fusion than Substance B.

Substance A has a lower specific heat capacity and a lower latent heat of fusion than Substance B.

Show answer & explanation

Answer: Substance A has a lower specific heat capacity and a higher latent heat of fusion than Substance B.

Answer

Substance A has a lower specific heat capacity and a higher latent heat of fusion than Substance B.

Specific heat capacity (

c

) measures the thermal energy required to raise the temperature of a given mass (

Q = mc\Delta T

). Under identical mass and heat supply, a steeper slope (faster temperature rise) signifies a lower specific heat capacity. Latent heat of fusion (

L_f

) governs the energy absorbed at a constant temperature during melting (

Q = mL_f

). A longer duration spent in the solid-to-liquid plateau indicates that a greater amount of energy was required to completely melt the sample, proving Substance A has a higher latent heat of fusion.

Step-by-Step Solution

1

Analyze the rate of temperature rise before phase change in relation to specific heat capacity.

The rate of temperature increase is inversely proportional to specific heat capacity (

c = \frac{Q}{m \Delta T}

). Because both samples have identical mass and heat input rates, a steeper temperature increase means Substance A requires less energy per degree change, indicating a lower specific heat capacity.

Specific heat capacity defines the amount of thermal energy required to raise the temperature of a unit mass by one degree.

2

Analyze the duration of the melting phase transition in relation to latent heat of fusion.

The energy absorbed during melting at constant temperature is given by

Q = m L_f

. Because the heating rate is constant, taking three times as long to melt means Substance A absorbs three times more energy during phase change, indicating a higher latent heat of fusion.

Latent heat of fusion defines the energy required to change a substance from solid to liquid at its melting point without a change in temperature.

3

Combine the deduced properties to determine the correct relationship.

Substance A possesses a lower specific heat capacity and a higher latent heat of fusion compared to Substance B.

Synthesizes the solid-state heating behavior and the isothermal phase transition behavior.

Key Concept

Relationship between heating curve slopes, specific heat capacity, and latent heat of fusion

Estimated Time:1m 30s

Physical Science

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