MCQ
The molar heat capacity in a process of a diatomic gas if it does a work of $\frac{Q}{4}$ when a heat of $Q$ is supplied to it is
- A$\frac{2}{5}R$
- B$\frac{5}{2}R$
- ✓$\frac{{10}}{3}R$
- D$\frac{6}{7}R$
✓
Answer
Correct option: C.
$\frac{{10}}{3}R$
c
(c) $dU = {C_V}dT = \left( {\frac{5}{2}R} \right)dT$or $dT = \frac{{2(dU)}}{{5R}}$…..$(i)$
From first law of thermodynamics
(c) $dU = {C_V}dT = \left( {\frac{5}{2}R} \right)dT$or $dT = \frac{{2(dU)}}{{5R}}$…..$(i)$
From first law of thermodynamics
$dU = dQ - dW$$ = Q - \frac{Q}{4}$$ = \frac{{3Q}}{4}$.
Now molar heat capacity $C = \frac{{dQ}}{{dT}} = \frac{Q}{{\frac{{2(dU)}}{{5R}}}} = \frac{{5RQ}}{{2\left( {\frac{{3Q}}{4}} \right)}} = \frac{{10}}{3}R$.
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