A student conducted a series of trials to study how the volume of a gas sample changes as … — ACT

A student conducted a series of trials to study how the volume of a gas sample changes as its temperature is varied under constant pressure. The data from the trials are shown in the table below:

Trial	Temperature ( $T$ , in $\text{K}$ )	Volume ( $V$ , in $\text{L}$ )
1	150	0.30
2	300	0.60
3	450	0.90
4	600	1.20

Based on these results, which of the following statements best describes the relationship between the temperature and volume of the gas sample, and identifies the correct proportionality constant, $k$ , for the equation $V = kT$ ?

A
Temperature and volume are inversely proportional, with $k = 45\text{ L}\cdot\text{K}$ .
Temperature and volume are directly proportional, with $k = 0.002\text{ L/K}$ .Cevap
C
Temperature and volume are directly proportional, with $k = 500\text{ K/L}$ .
D
Temperature and volume are inversely proportional, with $k = 0.002\text{ L/K}$ .

Cevap

Temperature and volume are directly proportional, with

k = 0.002\text{ L/K}

The correct answer states that temperature and volume are directly proportional with a constant of

0.002\text{ L/K}

. This is correct because as temperature (

T

) increases, volume (

V

) increases at a constant ratio. Solving for the proportionality constant in the equation

V = kT

gives

k = V/T = 0.30\text{ L} / 150\text{ K} = 0.002\text{ L/K}

Adım Adım Çözüm

Determine the type of relationship between temperature (

T

) and volume (

V

Observe that as temperature increases, volume also increases. Specifically, when temperature doubles from

150\text{ K}

300\text{ K}

, volume doubles from

0.30\text{ L}

0.60\text{ L}

. This indicates a direct relationship.

Recognizing whether a relationship is direct or inverse is necessary to select the correct equation format.

Calculate the constant of proportionality,

k

, using the direct proportionality equation

V = kT

Solve for

k

k = V/T

. Using the data from Trial 1,

k = 0.30\text{ L} / 150\text{ K} = 0.002\text{ L/K}

. Verifying with Trial 2,

k = 0.60\text{ L} / 300\text{ K} = 0.002\text{ L/K}

This determines the exact numerical value and units for the constant of proportionality.

Anahtar Kavram

Direct and Inverse Proportionality in Data Analysis

Tahmini Süre:1m 15s

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Cevap

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