Discussion
In the figure shown below, various thermodynamics processes for an ideal gas are represented. Match each curve with the process that it best represents.
Answer: C
The matching is aa' - Isothermal; bb' - Isentropic; cc' - Isobaric; dd' - Isochoric.
On a temperature-entropy diagram a horizontal line keeps the temperature fixed, so aa' is isothermal, and a vertical line keeps the entropy fixed, so bb' is isentropic.
Constant-volume and constant-pressure lines both rise to the right, with slopes
\[ \begin{aligned} \left(\frac{\partial T}{\partial s}\right)_{v} &= \frac{T}{c_{v}} \\ \left(\frac{\partial T}{\partial s}\right)_{p} &= \frac{T}{c_{p}} \end{aligned} \]
Since \(c_{p} \gt c_{v}\), the isochoric line is the steeper one. dd' is steeper than cc' through the common point, so dd' is isochoric and cc' isobaric.
The other options either swap the horizontal and vertical lines or swap the two sloping curves.
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