Heat and Thermodynamics 5 Question 21
22. An ideal gas is taken through the cycle $A \rightarrow B \rightarrow C \rightarrow A$, as shown in the figure. If the net heat supplied to the gas in the cycle is $5 J$, the work done by the gas in the process $C \rightarrow A$ is
(2002, 2M)
(a) $-5 J$
(b) $-10 J$
(c) $-15 J$
(d) $-20 J$
Show Answer
Solution:
- $\Delta W _{A B}=p \Delta V=(10)(2-1)=10 J$
$$ \Delta W _{B C}=0 $$
$($ as $V=$ constant $)$
From first law of thermodynamics
$$ \begin{aligned} \Delta Q & =\Delta W+\Delta U \\ \Delta U & =0 \quad \text { (process } A B C A \text { is cyclic) } \\ \therefore \quad \Delta Q & =\Delta W _{A B}+\Delta W _{B C}+\Delta W _{C A} \\ \therefore \quad \Delta W _{C A} & =\Delta Q-\Delta W _{A B}-\Delta W _{B C} \\ & =5-10-0=-5 J \end{aligned} $$
