Entropy for a Reversible Process

Q. Calculate the entropy change when 2 mol of an ideal gas expand isothermally and reversibly from an initial volume of 10 $c{m}^3$ to 100 $d{m}^3$ at 300 K.

1. 28.294 J K^-1

2. 38.294 J K^-1

3. 45 J K^-1

4. 50 J K^-1

Q. 1 mole of an ideal gas is allowed to expand isothermally at ${27}^{o}C$ until its volume is tripled. Calculate $△S_{sys}$ and $△S_{univ}$ under the reversible expansion.

1. $△S_{sys}=9.1J{K}^{-1}mo{l}^{-1}$
   
2. $△S_{univ}=△S_{sys}=9.1J{K}^{-1}mo{l}^{-1}$
3. $△S_{surr}=-9.1J{K}^{-1}mo{l}^{-1}$
4. $△S_{univ}=0$

Q. Calculate the change in entropy when $1$ mole nitrogen gas expands isothermally and reversibly from an initial volume of $1$ litre to a final volume of $10$ litre at ${27}^{o}C$.

Q. When one mole of an ideal gas is compressed to half of its initial volume and simultaneously heated to twice its initial temperature, the change in entropy of gas $\left(\Delta S\right)$ is:

1. $C_{p,m}ln2$
2. $C_{v,m}ln2$
3. $(C_{v,m}-R)ln2$
4. $Rln2$

Q. The equilibrium constant for the reaction given below is $2.0\times {10}^{-7}$ at 300 K. Calculate the standard entropy change if $△H^{\circ }=28.40kJmo{l}^{-1}$ for the reaction:
$PC{l}_5\left(g\right)\rightleftharpoons PC{l}_3\left(g\right)+C{l}_2\left(g\right)$

1. $-33.6Jmo{l}^{-1}{K}^{-1}$
2. $33.6Jmo{l}^{-1}{K}^{-1}$
3. $-43.6Jmo{l}^{-1}{K}^{-1}$
4. $43.6Jmo{l}^{-1}{K}^{-1}$

Q. When one mole of an ideal gas is compressed to half of its initial volume and simultaneously heated to twice its initial temperature, the change in entropy of gas $\left(\Delta S\right)$ is

1. $C_{p.m}$ ln 2
2. $C_{v.m}$ ln 2
3. R In 2
4. $(C_{v,m}-R)$ ln 2