Question

A gas at $25{}^{\circ }\text{C}$ with a volume of $6.5\text{L}$ expands by $50\%$, when the temperature is raised. If the pressure is kept constant, what is the final temperature of the gas?

• A. $320{}^{\circ }\text{C}$
• B. $198{}^{\circ }\text{C}$
• C. $125{}^{\circ }\text{C}$
• D. $174{}^{\circ }\text{C}$

Answer 1

The correct option is D $174{}^{\circ }\text{C}$

When the pressure of gas is kept constant, the volume of a gas is directly proportional to the temperature of the gas.

$\text{V}\propto \text{T}⟹\frac{\text{V}}{\text{T}}=\text{constant}$

$⟹\frac{{\text{V}}_1}{{\text{T}}_1}=\frac{{\text{V}}_2}{{\text{T}}_2}$

Given: ${\text{V}}_1=6.5\text{L}$ and ${\text{V}}_2$ is $50\%$ more than ${\text{V}}_1$, i.e. ${\text{V}}_2=1.5\times {\text{V}}_1=1.5\times 6.5=9.75\text{L}$

And ${\text{T}}_1=25{}^{\circ }\text{C}=25+273=298\text{K}$

$\therefore {\text{T}}_2=\frac{{\text{V}}_2}{{\text{V}}_1}{\text{T}}_1=\frac{9.75}{6.5}\times 298=447\text{K}$

In ${}^{\circ }\text{C}$, ${\text{T}}_2=447-273=174{}^{\circ }\text{C}$