Question

For irreversible expansion of ideal gas under isothermal condition, the correct option is:

• A. $\Delta U=0,\Delta S_{\text{total}}\ne 0$
• B. $\Delta U=0,\Delta S_{\text{total}}=0$
• C. $\Delta U=0,\Delta S_{\text{total}}=0$
• D. $\Delta U\ne 0,\Delta S_{\text{total}}\ne 0$

Answer 1

The correct option is A $\Delta U=0,\Delta S_{\text{total}}\ne 0$

As We know,
$\Delta U=n{C}_V\Delta T$
In the case of isothermal process, $\Delta T$ is zero. The value of $\Delta U$ is also zero from the relation.
$\Delta U=n{C}_V\Delta T$
Thus, for reversible and irreversible expansion for an ideal gas, under isothermal conditions, $\Delta U=0$. But the value $\Delta S$ for irreversible expansion of an ideal gas under isothermal conditions is not equal to zero.
The total entropy change ($\Delta S_{total})$ for the system and surroundings of a spontaneous process is given by
$\Delta S_{\text{total}}=\Delta S_{\text{system}}+\Delta S_{surrounding}>0$