Question

List - I (Process)	List - II
(I) Reversible isothermal expansion of an ideal gas.	(P) $\Delta S_{sys}=0$
(II) Reversible adiabatic compression of a real gas.	(Q) $\Delta H=\Delta U=\Delta S_{\text{total}}=0$
(III) Adiabatic free expansion.	(R) $\Delta S_{\text{total}}>0$
(IV) Isothermal free expansion	(S) $q=0$
	(T) $\Delta S_{\text{surr.}}=0$
	(U) $\Delta S_{sys}>0$

Which of the following options has the incorrect combination considering List - I and List - II.

• A. I - Q, U
• B. II - P, S, T
• C. III - R, S, T, U
• D. I - P, Q, U

Answer 1

The correct option is D I - P, Q, U

(I) $\to$ Q,U
(II) $\to$ P, S, T
(III) $\to$ R, S, T, U
(IV)$\to$ R, T, U
(I) For reversibale isothermal expansion:
$\Delta T=0,\Delta H=0,\Delta U=0,q\ne 0,$
$\Delta S_{\text{Total}}=0,\Delta S_{sys}>0,\Delta S_{\text{surr}}<0$
Hence (I) $\to Q,U$
For reversible adiabatic compression of a real gas :
$q=0,\Delta S_{\text{Total}}=0,\Delta S_{sys}=0,\Delta S_{\text{surr}}=0,$
$\Delta T\ne 0,\Delta H\ne 0,\Delta U\ne o$
Hence (II) $\to P,S,T$
(III) For Adiabatic Free expansion :
$q=0,w=0,\Delta U=0$
$\Delta H=0$ (for Ideal gas)
$\Delta H\ne 0$ (for other cases)
$\Delta S_{sys.}>0,\Delta S_{\text{surr.}}=0,\Delta S_{\text{Total}}>0$
Hence, (III) $\to R,S,T,U$
(IV) For Isothermal Free expansion :
$q\ne 0,w=0,\Delta U=0,\Delta T=0$
$\Delta H=0$ (for Ideal gas)
$\Delta H\ne 0$ (for other cases)
$\Delta S_{sys.}>0,\Delta S_{\text{surr.}}=0,\Delta S_{\text{Total}}>0$
Hence (IV) $\to R,T,U$