Heat and Thermodynamics 5 Question 36
37. One mole of an ideal gas in initial state $A$ undergoes a cyclic process $A B C A$, as shown in the figure. Its pressure at $A$ is $p _0$. Choose the correct option(s) from the following. (2010)
(a) Internal energies at $A$ and $B$ are the same
(b) Work done by the gas in process $A B$ is $p _0 V _0 \ln 4$
(c) Pressure at $C$ is $\frac{p _0}{4}$
(d) Temperature at $C$ is $\frac{T _0}{4}$
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Answer:
Correct Answer: 37. (b, d)
Solution:
- $T _A=T _B \Rightarrow \therefore \quad U _A=U _B$
$$ \begin{aligned} W _{A B} & =(1)(R) T _0 \ln \left(\frac{V _f}{V _i}\right) \\ & =R T _0 \ln \left(\frac{4 V _0}{V _0}\right)=p _0 V _0 \ln (4) \end{aligned} $$
Information regarding $p$ and $T$ at $C$ can not be obtained from the given graph. Unless it is mentioned that line $B C$ passes through origin or not.
Hence, the correct options are (a) and (b).
