# An ideal gas undergoes isothermal compression from

Question:

An ideal gas undergoes isothermal compression from $5 \mathrm{~m}^{3}$ against a constant external pressure of $4 \mathrm{Nm}^{-2}$. Heat released in this process is used to increase the temperature of 1 mole of $\mathrm{Al}$. If molar heat capacity of $\mathrm{Al}$ is $24 \mathrm{~J} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}$, the temperature of $\mathrm{Al}$ increases by :

1. $\frac{3}{2} \mathrm{~K}$

2. $\frac{2}{3} \mathrm{~K}$

3. $1 \mathrm{~K}$

4. $2 \mathrm{~K}$

Correct Option: , 2

Solution:

Work done on isothermal irreversible for ideal gas

$=-\mathrm{P}_{\mathrm{ext}}\left(\mathrm{V}_{2}-\mathrm{V}_{1}\right)$

$=-4 \mathrm{~N} / \mathrm{m}^{2}\left(1 \mathrm{~m}^{3}-5 \mathrm{~m}^{3}\right)$

$=16 \mathrm{Nm}$

Heat used to increase temperature of $\mathrm{A} \ell$

$\mathrm{q}=\mathrm{n} \mathrm{C}_{\mathrm{m}} \Delta \mathrm{T}$

$16 \mathrm{~J}=1 \times 24 \frac{\mathrm{J}}{\mathrm{mol} . \mathrm{K}} \times \Delta \mathrm{T}$

$\Delta \mathrm{T}=\frac{2}{3} \mathrm{~K}$