Thermodynamics and Thermochemistry - Result Question 16
16. An ideal gas undergoes isothermal compression from $5 m^{3}$ to $1 m^{3}$ against a constant external pressure of $4 $ $Nm^{-2}$. Heat released in this process is used to increase the temperature of $1$ mole of Al. If molar heat capacity of $Al$ is $24 $ $J$ $ mol^{-1} $ $K^{-1}$, the temperature of $Al$ increases by
(2019 Main, 10 Jan II)
(a) $\frac{3}{2} K$
(b) $1 K$
(c) $2 K$
(d) $\frac{2}{3} K$
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Answer:
Correct Answer: 16. (d)
Solution:
It is an irreversible isothermal compression of an ideal gas.
(i) $d E=d q+p\left(V _f-V _i\right)$
where, $d E=$ Internal energy change
$ \begin{aligned} d q & =\text { amount of heat released } \\ \Rightarrow 0 & =d q+p\left(V _f-V _i\right) \end{aligned} $
$[\because d E=0$ for an isothermal process $]$
$\Rightarrow d q=-4(1-5)=16 J$
(ii) $ d q=n \times C \times \Delta T$ (for $Al$ )
$\Rightarrow 16 J=1 $ $mol \times 24 $ $J$ $ mol^{-1} K^{-1} \times \Delta T$
$\Rightarrow \Delta T=\frac{16}{24} K=\frac{2}{3} K$
BETA
