Thermodynamics and Thermochemistry 1 Question 6
6. 5 moles of an ideal gas at $100 \mathrm{~K}$ are allowed to undergo reversible compression till its temperature becomes $200 \mathrm{~K}$. If $C_{V}=28 \mathrm{JK}^{-1} \mathrm{~mol}^{-1}$, calculate $\Delta U$ and $\Delta p V$ for this process. $\left(R=8.0 \mathrm{JK}^{-1} \mathrm{~mol}^{-1}\right)$
(2019 Main, 8 April II)
(a) $\Delta U=2.8 \mathrm{~kJ} ; \Delta(p V)=0.8 \mathrm{~kJ}$
(b) $\Delta U=14 \mathrm{~J} ; \Delta(p V)=0.8 \mathrm{~J}$
(c) $\Delta U=14 \mathrm{~kJ} ; \Delta(p V)=4 \mathrm{~kJ}$
(d) $\Delta U=14 \mathrm{~kJ} ; \Delta(p V)=18 \mathrm{~kJ}$
Show Answer
Solution:
- Given,
$$ \begin{aligned} n & =5 \mathrm{~mol}, T_{2}=200 \mathrm{~K}, T_{1}=100 \mathrm{~K} \ C_{V} & =28 \mathrm{JK}^{-1} \mathrm{~mol}^{-1} \ \Delta U & =n C_{V} \Delta T \ & =n C_{V}\left(T_{2}-T_{1}\right) \ & =5 \mathrm{~mol} \times 28 \mathrm{JK}^{-1} \mathrm{~mol}^{-1} \times(200-100) \mathrm{K} \ & =14,000 \mathrm{~J}=14 \mathrm{~kJ} \ \Delta p V & =n R \Delta T \ & =n R\left(T_{2}-T_{1}\right) \ & =5 \mathrm{~mol} \times 8 \mathrm{JK}^{-1} \mathrm{~mol}^{-1} \times(200-100) \mathrm{K} \ & =4000 \mathrm{~J}=4 \mathrm{~kJ} \end{aligned} $$
