Question

The temperature of $20litres$of nitrogen was increased from $100K$ to $300K$ at a constant pressure. The change in volume will be:
(A) $80litres$
(B) $60litres$
(C) $40litres$
(D) $20litres$

Answer 1

At constant pressure i.e. when the pressure remains constant, the volume of an ideal gas is directly proportional to the absolute temperature (Charle’s law). That means initial volume will be directly proportional to the initial temperature.

Complete step by step solution:
Given that,
The temperature of $20litres$ nitrogen is increased from $100K$ to $300K$at constant pressure.
So, let us consider,
The initial temperature of nitrogen is ${{T}_{1}}$.
The initial volume of nitrogen is ${{V}_{1}}$.
The final temperature of nitrogen is ${{T}_{2}}$.
The final volume of nitrogen is ${{V}_{2}}$.
So here,
Initial temperature of nitrogen i.e. ${{T}_{1}}$ is $100K$.
Initial volume of nitrogen i.e. ${{V}_{1}}$ is $20litres$.
Final temperature of nitrogen i.e. ${{T}_{2}}$ is $300K$.
But, Final volume of nitrogen i.e. ${{V}_{2}}$ is not given.
As we know,
According to Charle’s law, at constant pressure, the volume of an ideal gas is directly proportional to the absolute temperature i.e.
$V\propto T$
Hence, by applying Charle’s law equation i.e.
$\dfrac{{{V}_{1}}}{{{T}_{1}}}=\dfrac{{{V}_{2}}}{{{T}_{2}}}$
So, by applying this equation we can find out the final volume of nitrogen.
Thus, applying this equation we get,
$\dfrac{20}{100}=\dfrac{{{V}_{2}}}{300}$
where, ${{V}_{2}}=20\times 3litres=60litres$ of nitrogen.
Thus, the final volume of nitrogen i.e. ${{V}_{2}}$is $60litres$.
But the question demands to find out the change in volume of the nitrogen.
So, the change in volume of the nitrogen can be calculated by differentiating the initial and final volume of nitrogen.
So, the change in volume will be, $(60-20)litres=40litres$ of nitrogen.

Hence, the correct option is (C).

Note: Possibly, you can be confused with option B as it is the final volume of nitrogen but as per the question, we have to find the change in volume which can be calculated by differentiating the initial and final volume. As we know Charle’s law says that at constant pressure, the volume will be directly proportional to the temperature.