Heat and Thermodynamics 5 Question 4
4. $n$ moles of an ideal gas with constant volume heat capacity $C _V$ undergo an isobaric expansion by certain volume. The ratio of the work done in the process, to the heat supplied is
(a) $\frac{4 n R}{C _V+n R}$
(b) $\frac{4 n R}{C _V-n R}$
(c) $\frac{n R}{C _V-n R}$
(d) $\frac{n R}{C _V+n R}$
(2019 Main, 10 April I)
Show Answer
Solution:
- For isobaric process, work done is given as $W=n R \Delta T$
Heat supplied, $\Delta Q=n C _p \Delta T$ and
$$ \begin{array}{rlrl} & & C _p-\frac{C _V}{n} & =R \\ \Rightarrow \quad & \quad \frac{W}{\Delta Q} & =\frac{n R \Delta T}{n C _p \Delta T}=\frac{R}{C _p}=\frac{R}{R+\frac{C _V}{n}} \\ \therefore \quad & & \frac{W}{\Delta Q} & =\frac{n R}{n R+C _V} \end{array} $$
