A sample of ideal gas in a syringe occupies a volume of 300\text{ cm}^3 at a temperature o… — JAMB UTME

A sample of ideal gas in a syringe occupies a volume of $300\text{ cm}^3$ at a temperature of $27^\circ\text{C}$ . If the pressure of the gas remains constant, what is its volume in $\text{cm}^3$ when the temperature is raised to $127^\circ\text{C}$ ?

Answer: 400 cm³

Answer

400 cm³

According to Charles's Law, at constant pressure, the volume of a given mass of gas is directly proportional to its absolute temperature (

V \propto T

). Converting the given temperatures to kelvins yields

T_1 = 300\text{ K}

and

T_2 = 400\text{ K}

. Applying

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

gives

V_2 = \frac{300 \times 400}{300} = 400\text{ cm}^3

Step-by-Step Solution

Convert the initial and final temperatures from degrees Celsius to kelvins.

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

and

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

Gas law calculations require absolute temperature measured on the kelvin scale.

Apply Charles's Law, which relates volume and absolute temperature at constant pressure.

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

The pressure of the gas is maintained constant.

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

V_2

\frac{300\text{ cm}^3}{300\text{ K}} = \frac{V_2}{400\text{ K}} \implies V_2 = 400\text{ cm}^3

Cross-multiplying gives

V_2 = \frac{300 \times 400}{300} = 400\text{ cm}^3

Key Concept

Charles's Law

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