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  • Figure is the P − V diagram for a Carnot cycle. In this diagram, <img alt="" src="https://cdn.entrance360.com/media/uploads/2023/08/19/phy-f56-q61.PNG" style="height:125px; width:16

Figure is the P − V diagram for a Carnot cycle. In this diagram,

Option: 1

Curve DA represents isothermal process and BC adiabatic process


Option: 2

Curve AB represents adiabatic process and BC isothermal process


Option: 3

Curve CD represents isothermal process and DA adiabatic process


Option: 4

Curve CD represents adiabatic process and DA isothermal process


Answers (1)

best_answer

For adiabatic process, \mathrm{P V^\gamma=} constant. Differentiating w.r.t V we get

\mathrm{\begin{aligned} & \frac{d P}{d V} V^\gamma+P \gamma V^{\gamma-1}=0 \\ & \text { Or } \frac{d P}{d V}=-\frac{\gamma P}{V} \end{aligned}}

For isothermal process, PV = constant. Hence

\mathrm{\frac{d P}{d V}=-\frac{P}{V}}

Now, dP/dV is the slope of the (P − V)graph. Thus the slope of the (P − V) graph for an
adiabatic process is γ times that for an isothermal process. Hence curves BC and DA
both represent adiabatic process and curves AB and CD both represent isothermal
process.

Posted by

Shailly goel

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