Question

$1$ mole of an ideal gas is expanded from an initial pressure of $1$ bar to final pressure of $0.1$ bar at constant temperature of $273K$. Predict which of the following is not true?

• A. $\Delta E=0$
• B. $\Delta H=0$
• C. $PV$ is constant
• D. $\Delta S<0$

Answer 1

The correct option is D $\Delta S<0$

Given

1 mole of ideal gas

Constant temp = 273K

Initial pressure = 1 bar

Final pressure = 0.1 bar

Solution

Using First Law of thermodynamics

$\Delta H=\Delta U+W$

W= work done

$\Delta H=n\ast C_p\ast dT$

$\Delta U=n\ast C_v\ast dT$

As Temperature is constant dT =0

Therefore

$\Delta H=0$

$\Delta U=0$

Putting values in first law

W=0

We know that $W=PdV$

Hence PdV=0

This shows PV=constant

Therefore only Option D is not true

The correct option is D