One mole of an ideal gas in initial state A undergoes a cyclic process ABCA, as shown in the figure. Its pressure at A is \(P_{0}\). Choose the correct option from the following.
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Points A and B lie on the same isotherm, so the process AB is isothermal expansion.
Work done by the gas in process AB is \(P_{0}V_{0}\ln (4)\)
Pressure at C is \(\frac{P_{0}}{4}\)
Temperature at C is \(\frac{T_{0}}{4}\)
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The Correct Option isB
Solution and Explanation
Step 1: Understanding the Concept
On the P-V diagram A and B are at the same temperature, so AB is an isothermal expansion and the internal energy of an ideal gas does not change.
Step 2: Check option A
Internal energy depends only on temperature, so it is equal at A and B. Option A is wrong.
Step 3: Check option B
Isothermal work \(W=nRT\ln\dfrac{V_B}{V_A}\). For one mole at A, \(RT_0=P_0V_0\), and the volume ratio is 4, so \(W=P_0V_0\ln 4\). Option B is correct.
Step 4: Check options C and D
The pressure and temperature at C do not follow from the figure with these values, so they cannot be taken as correct. Option (B) is the correct statement.
Final Answer:
The work done by the gas in process AB is \(P_0V_0\ln 4\).
\[ \boxed{\text{(B) }\text{Work done by the gas in process AB is } P_0V_0\ln(4)} \]
