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) $-20 J$

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Answer:

Correct Answer: 22. (a)

Solution:

  1. $\Delta W _{A B}=p \Delta V=(10)(2-1)=10 J$

$$ \Delta W _{B C}=0 $$

$($ as $V=$ constant $)$

From first law of thermodynamics

$$ \begin{aligned} \Delta Q & =\Delta W+\Delta U \\ \Delta U & =0 \quad \text { (process } A B C A \text { is cyclic) } \\ \therefore \quad \Delta Q & =\Delta W _{A B}+\Delta W _{B C}+\Delta W _{C A} \\ \therefore \quad \Delta W _{C A} & =\Delta Q-\Delta W _{A B}-\Delta W _{B C} \\ & =5-10-0=-5 J \end{aligned} $$



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