A fixed mass of hydrogen gas occupies a volume of 600\text{ cm}^3 at 27^\circ\text{C}. Wha… — JAMB UTME

A fixed mass of hydrogen gas occupies a volume of $600\text{ cm}^3$ at $27^\circ\text{C}$ . What is its volume in $\text{cm}^3$ when the temperature is raised to $127^\circ\text{C}$ at constant pressure?

Answer: 800 cm³

Answer

800

Converting initial and final temperatures to Kelvin gives

300\text{ K}

and

400\text{ K}

respectively. Applying Charles's Law (

V_1 / T_1 = V_2 / T_2

) gives

V_2 = 600 \times (400 / 300) = 800\text{ cm}^3

Step-by-Step Solution

Convert given temperatures from Celsius to Kelvin

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

and

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

Charles's Law requires temperature values to be expressed on the absolute (Kelvin) temperature scale.

Set up Charles's Law formula relating volume and absolute temperature

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

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

Substitute the initial volume and absolute temperatures into the formula

V_2 = 600 \times \frac{400}{300} = 800\text{ cm}^3

Simplifying the expression yields the final gas volume.

Key Concept

Charles's Law and Absolute Temperature Scale

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