TS EAMCET · Physics · Thermodynamics
Three moles of an ideal gas undergoes a cyclic process ABCA as shown in the figure. The pressure, volume and absolute temperature at points \(\mathrm{A}, \mathrm{B}\) and C are respectively \(\left(\mathrm{P}_1, \mathrm{~V}_1\right.\), \(\left.T_1\right),\left(P_2, 3 V_1, T_1\right)\) and \(\left(P_2, V_1, T_2\right)\). Then the total work done in the cycle ABCA is (R- Universal gas constant).
- A \(\mathrm{RT}_1[3 \ln (3)+2]\)
- B \(\mathrm{RT}_1[3 \ln (2)]\)
- C \(3 \mathrm{RT}_1(\ln 3)\)
- D \(\mathrm{RT}_1[3 \ln (3)-2]\)
Answer & Solution
Correct Answer
(D) \(\mathrm{RT}_1[3 \ln (3)-2]\)
Step-by-step Solution
Detailed explanation
Work done for AB (isothermal): \(W_{AB} = nRT_1 \ln \left(\frac{V_B}{V_A}\right) = 3RT_1 \ln \left(\frac{3V_1}{V_1}\right) = 3RT_1 \ln(3)\) Work done for BC (isobaric): \(W_{BC} = P_2(V_C - V_B) = P_2(V_1 - 3V_1) = -2P_2 V_1\) From ideal gas law at B:…
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