Question

A closed cylindrical vessel contains $N$ moles of an ideal diatomic gas at a temperature $T$. On supplying heat, temperature remains same, but $n$ moles get dissociated into atoms. The heat supplied is

• A. $\frac{5}{2}(N-n) R T$
• B. $\frac{5}{2} n R T$
• C. $\frac{1}{2} n R T$
• D. $\frac{3}{2} n R T$

Answer 1

Answer: (C)

Heat supplied $=\Delta U=U_{\text {final }}-U_{\text {initial }}$
[Only diatomic gas is present]
Total intemal energy initially $=\frac{5}{2} N R T$
Total internal energy when
'$n$' moles get dissociated $=\frac{5}{2}(N-n) R T+\frac{3}{2}(2 n) R T$
[diatomic and monoatomic both are present]
$\Delta U=\left\{\frac{5}{2}(N-n) R T+\frac{3}{2}(2 n) R T\right\}-\frac{5}{2} N R T$
Solving this we get
$\Delta U=\frac{1}{2} n R T$
$\therefore $ Heat supplied is $\frac{1}{2} n R T$.