Question

The isothermal modulus of elasticity $\left(B\right)$ of a sample of gas depends upon

• A. temperature
• B. volume
• C. atomicity of gas
• D. pressure of gas

Answer 1

The correct option is D pressure of gas

Using ideal gas equation:
$PV=nRT$
As given in the question, we need to find isothermal modulus of elasticity. So, temperature is treated constant.
$\Rightarrow T=$ constant
$\Rightarrow PV=$ constant

After small increase in pressure and volume of gas:
$PV=(P+\Delta P)(V+\Delta V)$
$PV=PV+\Delta PV+P\Delta V+\Delta P\Delta V$
Here, $\Delta P\Delta V$ is very small, hence neglected.
$0=\Delta PV+P\Delta V$
$-\Delta PV=P\Delta V$
$\frac{-\Delta P}{\Delta V/V}=P\Rightarrow B$
$\therefore B=P$