Question

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

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

Answer 1

Answer: (B)

$\frac{2}{3}K$

Work Done on isothermal irreversible for ideal gas

$W=-P_{ext}(V_2-V_1)=-P^{}ext\times \Delta V=-4N.m^{-2}\times (1-5)m^3$

$=-4N.m^{-2}\times -4m^3=16N.m$

For Isothermal process , $\Delta U=0$

$q=-16J$

Heat used to increase temperature

$q=n{C}_m\Delta T$

$n=1;C_m=24J/(mol.K)$

Substituting the Values , we get

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