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 correct combination considering List - I and List - II.

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

Answer 1

The correct option is C $III-R,S,T,U$

(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 $\left(I\right)\to Q,U$
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 $\left(II\right)\to P,S,T$
(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 $\left(III\right)\to R,S,T,U$
(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 $\left(IV\right)\to R,T,U$