Question

$1$ mole of $N{H}_3$ gas at ${27}^o$C is expanded adiabatic condition to make volume $8$ times $(\gamma =1.33)$. Find temperature and work done respectively.

• A. $150$ K, $900$ cal
• B. $150$ K, $400$ cal
• C. $250$ K, $1000$ cal
• D. $200$ K, $800$ cal

Answer 1

The correct option is A $150$ K, $900$ cal

$T{V}^{\gamma -1}=$ Constant [Adiabatic condition]

$\left(T_2\right)(V_2{)}^{0.33}=(T_1\left)\right(V_1{)}^{0.33}$

$V_2=8V_1$

$\therefore T_2=\frac{T_1}{(8{)}^{0.33}}=\frac{300}{(8{)}^{0.33}}\approx 150K$

$W=\frac{nR(T_2-T_1)}{\gamma -1}$

$=-\frac{1\times 2\times 150}{0.33}Cal\approx 900Cal$

Work done $=900Cal$