One mole of an ideal gas at an initial temperature of ' $T$ ' K does ' 6 R ' of work adiabatically. If the…
One mole of an ideal gas at an initial temperature of ' $T$ ' K does ' 6 R ' of work adiabatically. If the ratio of specific heats of this gas at constant pressure and at constant volume is $5 / 3$, the final temperature of gas will be ($\left.\mathrm{R}=8.31 \mathrm{~J} \mathrm{~mole}^{-1} \mathrm{~K}^{-1}\right)$
$(T+4 \cdot 2) K$
$(\mathrm{T}-4 \cdot 2) \mathrm{K}$
$\quad(T+4) K$
$(T-4) K$
Solution
For an adiabatic process,
$\mathrm{W}=\frac{\mathrm{nR}\left(\mathrm{~T}_{\mathrm{i}}-\mathrm{T}_{\mathrm{f}}\right)}{\gamma-1}$
$\begin{array}{ll}\therefore \quad & 6 R=\frac{R\left(T-T_f\right)}{\left(\frac{5}{3}-1\right)} \quad \ldots .\text{(Given: } \mathrm{n}=1) \\ \therefore & T_f=(T-4) K\end{array}$