TS EAMCET · Physics · Thermodynamics

An ideal gas goes through a process \(A \rightarrow B \rightarrow C \rightarrow A\) cycle. The process, \(A \rightarrow B\) is adiabatic. Calculate the work done in the process \(A \rightarrow B\).

A \(p_0 V_0\)
B \(\frac{p_0 V_0\left(2^{1 / \gamma}-2\right)}{(1-\gamma)}\)
C \(p_0 V_0 \ln (2)\)
D \(\frac{p_0 V_0\left(2^{1 / \gamma}-1\right)}{(\gamma-1)}\)

Verified Solution

Answer & Solution

Correct Answer

(B) \(\frac{p_0 V_0\left(2^{1 / \gamma}-2\right)}{(1-\gamma)}\)

Step-by-step Solution

Detailed explanation

We know that, adiabatic relation, \( p V^\gamma=\text { constant } \) For adiabatic process \(A \rightarrow B\) \( \begin{aligned} 2 p_0 V_0^\gamma & =p_0 V_1^\gamma \\ \Rightarrow \quad V_1^\gamma & =2 V_0^\gamma \Rightarrow V_1=2^{1 / \gamma} V_0 \end{aligned} \)…

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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