Question

A closed container is filled with $20\text{moles}$ of an ideal diatomic gas at absolute temperature $T$. When heat is supplied to it, the temperature remains constant, but $8\text{moles}$ of the gas dissociate into atoms. The heat energy supplied to the gas is

• A. $7RT$
• B. $6RT$
• C. $4RT$
• D. $5RT$

Answer 1

The correct option is C $4RT$

Initial internal energy,
$U_i=\frac{nfRT}{2}=\frac{20\times 5\times RT}{2}=50RT$
[for diatomic gas, $f=5$]

Final internal energy,
$U_f=\frac{n_1{f}_{1}RT}{2}+\frac{n_2{f}_{2}RT}{2}$
$\Rightarrow U_f=\frac{12\times 5\times RT}{2}+\frac{2\times 8\times 3\times RT}{2}=54RT$
[if one mole of diatomic gas dissociates, then two moles of monatomic gas are produced, and for monoatomic gas, $f=3$]

Now, change in internal energy will be,
$\Delta U=U_f-U_i=54RT-50RT=4RT$
Since there is no volume change associated with the process, work done $W=0$
Hence, heat supplied $Q=\Delta U=4RT$
[from first law of thermodynamics]