COMEDK · Physics · 13. Thermodynamics

Carnot cycle of an engine is given below

Total work done by the gas in one cycle is

A \(\mu R T_{2} \log \dfrac{V_{2}}{V_{1}}-\mu R T_{1} \log \dfrac{V_{3}}{V_{4}}\)
B \(\mu R T_{1} \log \dfrac{V_{2}}{V_{1}}-\mu R T_{2} \log \dfrac{V_{3}}{V_{4}}\)
C \(\mu R T_{1} \log \dfrac{V_{2}}{V_{1}}+\mu R T_{2} \log \dfrac{V_{3}}{V_{4}}\)
D Zero

Verified Solution

Answer & Solution

Correct Answer

(B) \(\mu R T_{1} \log \dfrac{V_{2}}{V_{1}}-\mu R T_{2} \log \dfrac{V_{3}}{V_{4}}\)

Step-by-step Solution

Detailed explanation

The Carnot cycle has two isothermal and two adiabatic processes. \(P \to Q\): Isothermal expansion at \(T_1\) (\(T_1 = T_2\)): \(W_{PQ} = \mu RT_1 \ln\dfrac{V_2}{V_1}\) \(Q \to R\): Adiabatic expansion: \(W_{QR} = \dfrac{\mu R(T_2 - T_3)}{\gamma - 1}\) \(R \to S\): Isothermal…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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Carnot cycle of an engine is given belowTotal work done by the gas in one cycle is

Step-by-step Solution

Carnot cycle of an engine is given below

Total work done by the gas in one cycle is