Question

A gas at $27{}^{\circ }\text{C}$ with a volume of $5\text{L}$ expands by $45\%$, when the temperature is raised. If the pressure is kept constant, what is the final temperature of the gas?

• A. 162

Answer 1

The correct option is A 162
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: ${\text{V}}_1=5\text{L}$ and ${\text{V}}_2$ is $45\%$ more than ${\text{V}}_1$, i.e. ${\text{V}}_2=1.45\times {\text{V}}_1=1.45\times 5=7.25\text{L}$

And ${\text{T}}_1=27{}^{\circ }\text{C}=27+273=300\text{K}$

$\therefore {\text{T}}_2=\frac{{\text{V}}_2}{{\text{V}}_1}{\text{T}}_1=\frac{7.25}{5}\times 300=435\text{K}$

In ${}^{\circ }\text{C}$, ${\text{T}}_2=435-273=162{}^{\circ }\text{C}$