Question

An ideal gas undergoes isothermal compression from $5 \,m^3$ 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 :

• A. $\frac{3}{2} K$
• B. $\frac{2}{3} K$
• C. $1 K$
• D. $2 K$

Answer 1

Answer: (B)

Work done on isothermal irreversible for ideal gas
$= -P_{ext } \left(V_{2} -V_{1}\right)$
$ =-4 N/m^{2} \left(1m^{\frac{1}{3}} - 5m^{3}\right) $
$=16Nm$
Isothermal process for ideal gas
$ \Delta U =0$
$ q=-w $
$= -16 Nm $
$=-16 J $
Heat used to increase temperature of $ A\ell $
$q=n C_{m}\Delta T $
$ 16J =1 \times24 \frac{J}{\text{mol}.K} \times\Delta T$
$ \Delta T = \frac{2}{3} K $