A sample of argon gas occupies a volume of 400\text{ cm}^3 at a temperature of -23^\circ\t… — JAMB UTME

A sample of argon gas occupies a volume of $400\text{ cm}^3$ at a temperature of $-23^\circ\text{C}$ . If the pressure remains constant and the gas expands to a volume of $600\text{ cm}^3$ , what is its final temperature in degrees Celsius ( $^\circ\text{C}$ )?

Answer: 102 °C

Answer

102 °C

Converting the initial temperature to Kelvin gives

T_1 = -23 + 273 = 250\text{ K}

. Applying Charles's Law

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

gives

T_2 = \frac{600 \times 250}{400} = 375\text{ K}

. Subtracting

273

converts this back to degrees Celsius:

375 - 273 = 102^\circ\text{C}

Step-by-Step Solution

Convert initial temperature from Celsius to Kelvin

T_1 = 250\text{ K}

Gas laws require temperature to be expressed on the absolute (Kelvin) scale.

Calculate final absolute temperature using Charles's Law

T_2 = \frac{600\text{ cm}^3 \times 250\text{ K}}{400\text{ cm}^3} = 375\text{ K}

At constant pressure, volume is directly proportional to absolute temperature (

V_1/T_1 = V_2/T_2

Convert final temperature back to degrees Celsius

t_2 = 375 - 273 = 102^\circ\text{C}

The question explicitly requests the final answer in degrees Celsius.

Key Concept

Charles's Law states that the volume of a fixed mass of gas is directly proportional to its absolute temperature at constant pressure (

V \propto T

). Temperatures must always be converted to Kelvin (

K = ^\circ\text{C} + 273

) prior to calculation.

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