Question

The volume of an ideal gas is $1 L$ and its pressure is equal to $72 cm$ of mercury column. The volume of gas is made $900\,c{m^3}$ by compressing it isothermally. The stress of the gas will be
A) 4 cm (mercury)
B) 8 cm (mercury)
C) 18 cm (mercury)
D) 12 cm (mercury)

Answer 1

Hint
In this question we need to find the stress or the pressure developed by the gas in terms of the height of mercury. We will use the gas equation. Values of all the quantities except for one are known and substitute the values to find the missing variable.

Complete step-by-step answer
For an isothermal, the temperature during the course of action will remain constant i.e. it will not change. From the gas laws, we know the relation:
$\dfrac{{pV}}{{RT}} = k$
Where, $k$ is a constant,
$p$ is the pressure of the gas,
$V$ is the volume of the gas,
$R$ is the universal gas constant,
And $T$ is the temperature of the gas.
As for an isothermal process, the temperature of the process remains constant,
$pV{\text{ }} = {\text{ }}k$
Equating this to the final state of the process,
${p_1}{V_1}\, = \,{p_1}{V_1}$
${p_2}{\text{ }} = {\text{ }}\dfrac{{{p_1}{V_1}}}{{{V_2}}}$
${p_2}{\text{ }} = {\text{ }}\dfrac{{72{\text{ }} \times {\text{ }}1000}}{{9000}} \\\ {p_2}\, = \,80\,cm \\\$
Therefore the change in pressure or stress developed is $80\, - \,72 = 8cm$
So, the option with the correct answer is option B.

Note
Stress and pressure both have the same formula which is force per unit area and they are often used interchangeably. Don’t get confused or scared by the word “stress”.