Question

If three identical samples of an ideal gas initialy compressed at same state $(P_0,V_0,T_0)$ to half their volumes by three different process

I: by the irreversible adiabatic compression against constant external pressure.
II: by the isothermal irreversible process.
III: by the reversible adiabatic process.
Then, in the graph shown, the final state is represented by three different points. identify the incorrect statement.

• A. $\Delta S_{sys}=0$, corresponding to the final state 1
• B. $\Delta S_{surr}=0,$ corresponding to the final state 3
• C. $\Delta U=0$ corresponding to the final state 2
• D. $\Delta U$ will be maximum for irreversible adiabatic compression

Answer 1

The correct option is A $\Delta S_{sys}=0$, corresponding to the final state 1

Point 1: Corresponds to the irreversible adiabatic process for which $\Delta S_{sys}>0,\Delta S_{surr}=0,\Delta S_{univ}>0,\Delta U\ne 0(\because \Delta T\ne 0)$
Point 2: Corresponds to the reversible adiabatic process, for which
$\Delta S_{sys}=0,\Delta S_{Surr}=\Delta S_{univ}=0,\Delta U\ne 0(\because \Delta T\ne 0)$
Point 3 : Corresponds to the irreversible isothermal process, for which $\Delta U=0(\because \Delta T=0)$
$\Delta T$ will be maximum for irreversible adiabatic process. So $\Delta U$ will be maximum for irreversible adiabatic process.