Heat and Thermodynamics 5 Question 13
14. Two moles of an ideal monoatomic gas occupies a volume $V$ at $27^{\circ} C$. The gas expands adiabatically to a volume $2 V$. Calculate (i) the final temperature of the gas and (ii) change in its internal energy.
(2018 Main)
(a) (i) $195 K$ (ii) $2.7 kJ$
(b) (i) $189 K$ (ii) $2.7 kJ$
(c) (i) $195 K$ (ii) $-2.7 kJ$
(d) (i) $189 K$ (ii) $-2.7 kJ$
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Solution:
- For adiabatic process,
$$ \begin{aligned} T _1 V _1^{\gamma-1} & =T _2 V _2^{\gamma-1} \quad\left(\because \gamma=\frac{5}{3}\right) \\ \Rightarrow \quad 300(V)^{\frac{2}{3}} & =T _2(2 V)^{\frac{2}{3}} \Rightarrow T _2=\frac{300}{2^{\frac{2}{3}}} \approx 189 K \\ \Delta U=\frac{f}{2} n R \Delta T & =\left(\frac{3}{2}\right)(2)\left(\frac{25}{3}\right)(189-300) \\ & =-2.7 kJ \end{aligned} $$
