A flexible balloon contains a sample of gas occupying a volume of 3.0\text{ m}^3 at a temp… — JAMB UTME

A flexible balloon contains a sample of gas occupying a volume of $3.0\text{ m}^3$ at a temperature of $27^\circ\text{C}$ under constant pressure. If the gas is heated to $127^\circ\text{C}$ while keeping the pressure constant, what is the new volume of the gas in $\text{m}^3$ ?

Answer: 4 m³

Answer

The new volume of the gas is

4.0\text{ m}^3

According to Charles's Law (

\frac{V_1}{T_1} = \frac{V_2}{T_2}

), at constant pressure, volume is directly proportional to absolute temperature in Kelvin. Converting

27^\circ\text{C}

300\text{ K}

and

127^\circ\text{C}

400\text{ K}

yields a final volume

V_2 = 3.0 \times \frac{400}{300} = 4.0\text{ m}^3

Step-by-Step Solution

Convert the given initial and final temperatures from Celsius to Kelvin

T_1 = 27 + 273 = 300\text{ K}

and

T_2 = 127 + 273 = 400\text{ K}

Gas law calculations require absolute temperature in Kelvin.

Set up Charles's Law equation for constant pressure processes

\frac{V_1}{T_1} = \frac{V_2}{T_2}

At constant pressure, the volume of a given mass of gas is directly proportional to its absolute temperature.

Substitute the values into the equation and solve for the final volume

V_2

V_2 = 3.0 \times \frac{400\text{ K}}{300\text{ K}} = 4.0\text{ m}^3

Direct algebraic evaluation yields the final gas volume.

Key Concept

Charles's Law

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