Question

Match the thermodynamic processes given below:

$\begin{array}{cc}\text{Column I}& \text{Column II}\\ \text{A. Freezing of water at 273K and 1 atm}& \text{p. q=0}\\ \text{B. Expansion of 1 mole of an ideal gas into a vacuum under isolated conditions}& \text{q. W=0}\\ \text{C. Mixing of equal volumes of two ideal gases at constant temperature and pressure in an isolated container}& \text{r. ΔSsys<0}\\ \text{D. Reversible heating of H2(g) at 1 atm from 300 K to 600K, followed by reversible cooling to 300K at 1 atm}& \text{s. ΔU=0}\\ & \text{t. ΔG=0}\end{array}$

• A. $\left(A\right)\to r,t;\left(B\right)\to q,s,t;\left(C\right)\to p,q,s;\left(D\right)\to p,q,s$
• B. $\left(A\right)\to r,t;\left(B\right)\to p,q,s;\left(C\right)\to p,q,s;\left(D\right)\to q,s,t$
• C. $\left(A\right);\to q,s,t\left(B\right)\to p,q,s;\left(C\right)\to p,q,s;\left(D\right)\to r,t$
• D. $\left(A\right)\to r,t;\left(B\right)\to p,q,s;\left(C\right)\to p,q,s;\left(D\right)\to q,s,t$

Answer 1

The correct option is B

$\left(A\right)\to r,t;\left(B\right)\to p,q,s;\left(C\right)\to p,q,s;\left(D\right)\to q,s,t$

$\left(A\right)\to r,t;\left(B\right)\to p,q,s;\left(C\right)\to p,q,s;\left(D\right)\to q,s,t$
(A) $H_{2}O\left(l\right)$ $H_{2}O\left(s\right))$
Q < 0, W < 0 (expansion)
$\Delta U=0$
$\because T_i=T_f,\Delta G=0$ $\Delta S_{sys}<0$ (solid state is more ordered than liquid state)
$\Delta U<0;\Delta G=0$ (At equilibrium)
(B) q = 0 (isolated), W = 0 $(P_{ext}=0)$
$\Delta S_{sys}>0\because V_2>V_1$
$\Delta U=0\because q=W=0$
$\Delta G<0\because p_2<p_1$
(C) q = 0 (isothermal mixing of ideal gases at constant p)
$W=0\because \Delta U=0;q=0,\Delta S_{sys}>0$
$\because V_2>V_1,\Delta U=0$
$\because \Delta T=0$
$\Delta G<0\because$ mixing is spontaneous.
(D) q = 0 (returning to same state and by same path)
W = 0
$\Delta S_{sys}=0$ (same initial and final states)
$\Delta U=0$
$\because T_i=T_f,\Delta G=0$