Heat and Thermodynamics 6 Question 8
12. The $p-T$ diagram for an ideal gas is shown in the figure, where $A C$ is an adiabatic process, find the corresponding $p-V$ diagram
(2003, 2M)
(a)
(b)
(c)
(d)
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Answer:
Correct Answer: 12. (none)
Solution:
- Out of the alternatives provided, none appears completely correct.
$A B$ is an isothermal process.
( $T=$ constant, $p \propto \frac{1}{V}$ ). So, $p-V$ graph should be rectangular hyperbola with $p$ decreasing and $V$ increasing.
$B C$ is an isobaric process.
( $p=$ constant, $V \propto T$ ). Temperature is increasing. Hence, volume should also increase. $C A$ is an adiabatic process $\left(p V^{\gamma}=\right.$ constant). Pressure is increasing. So, volume should decrease. At point $A$, an isotherm $A B$ and an adiabatic curve $A C$ are meeting.
We know that
(slope of an adiabatic graph in $p-V$ diagram $)=\gamma($ slope of an isothermal graph in the same diagram) with $\gamma>1$ or
(Slope $) _{\text {adiabatic }}>(\text { Slope }) _{\text {isothermal }}$.
None of the given examples fulfill all the above requirements.
