Thermodynamics and Thermochemistry - Result Question 6
6. $5$ moles of an ideal gas at $100 K$ are allowed to undergo reversible compression till its temperature becomes $200 K$. If $C _V=28 $ $JK^{-1}$ $ mol^{-1}$, calculate $\Delta U$ and $\Delta p V$ for this process. $(R=8.0 $ $JK^{-1}$ $ mol^{-1})$
(2019 Main, 8 April II)
(a) $\Delta U=2.8 $ $ kJ ; \Delta(p V)=0.8 $ $kJ$
(b) $\Delta U=14$ $ J ; \Delta(p V)=0.8 $ $J$
(c) $\Delta U=14 $ $kJ ; \Delta(p V)=4$ $ kJ$
(d) $\Delta U=14$ $ kJ ; \Delta(p V)=18$ $ kJ$
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Answer:
Correct Answer: 6. (c)
Solution:
Given,
$n =5 $ $mol, T _2=200 K, T _1=100 K $
$C _V =28 JK^{-1} $ $mol^{-1} $
$\Delta U =n C _V \Delta T $
$ =n C _V\left(T _2-T _1\right) $
$ =5 $ $mol \times 28 JK^{-1} $ $mol^{-1} \times(200-100) K $
$ =14,000 J=14 kJ $
$\Delta p V =n R \Delta T $
$ =n R\left(T _2-T _1\right) $
$ =5 $ $mol \times 8 JK^{-1} $ $mol^{-1} \times(200-100) K $
$=4000 J=4 kJ$
BETA
