Question

A gas filled in a container of volume V at ${{121}^{\circ }}C$. To what temperature should it be heated in order that $\dfrac{1}{4}th$of the gas escape out of the vessel?

Answer 1

This question can be solved easily using Charles law. Hence we have to know the Charles law. That is, also known as the law of volumes. According to the experimental results with gases the Charles law states that the gas expands with the increase in temperature. Hence we can say that the volume of the gas and temperature are directly proportional.

Formula used:
Using Charles law we have,
$\dfrac{V}{T}=k$
Where V is the volume of the gas
T is the temperature
K is the proportionality constant

Complete step-by-step solution:
Using Charles law we have, the volume of the expanded gas is directly proportional to the temperature. Hence,
$\dfrac{V}{T}=k$
Where V is the volume of the gas
T is the temperature
K is the proportionality constant
The above equation can be expanded as,
$\dfrac{{{V}_{1}}}{{{T}_{1}}}=\dfrac{{{V}_{2}}}{{{T}_{2}}}$
Given that,
${{V}_{1}}=V$
${{V}_{2}}=\dfrac{V}{4}$
${{T}_{1}}={{121}^{\circ }}C$
Here we have to find the temperature ${{T}_{2}}$. Thus by rearranging the equation we get,
${{T}_{2}}=\dfrac{{{V}_{2}}}{{{V}_{1}}}\times {{T}_{1}}$
Then by substituting the values the equation becomes,
${{T}_{2}}=\dfrac{\dfrac{V}{4}}{V}\times {{121}^{\circ }}C$
$\begin{aligned} & \Rightarrow {{T}_{2}}=\dfrac{1}{4}\times {{121}^{\circ }}C \\\ & \therefore {{T}_{2}}={{30.25}^{\circ }}C \\\ \end{aligned}$

Note: The ideal gas law is the general gas equation. It describes the equation of state of an ideal gas. This law is formed by the combination of Boyle’s law, Charles law, Avagadro’s law and Gay Lussac’s law. This law will not have any comment whether it heats or cools during its expansion or compression. These laws are applied to various thermodynamic processes.