KCET · Chemistry · Thermodynamics (C)

Based on the first law of thermodynamics, which one of the following is correct?

A For an isochoric process \(=\Delta \mathrm{E}=-\mathrm{q}\)
B For an adiabatic process \(=\Delta \mathrm{E}=-\mathrm{W}\)
C For an isothermal process \(=\mathrm{q}=+\mathrm{w}\)
D For a cyclic process \(q=-w\)

Verified Solution

Answer & Solution

Correct Answer

(D) For a cyclic process \(q=-w\)

Step-by-step Solution

Detailed explanation

First law of Thermodynamics is
\[
\Delta \mathrm{E}=\mathrm{Q}+\mathrm{W}
\]
(a) For isochoric process, \(\Delta V=0\)
\[
\mathrm{W}=\mathrm{p} \Delta \mathrm{V}=0
\]
\(\therefore\)
\[
\Delta \mathrm{E}=\mathrm{Q}
\]
(b) For adiabatic process, \(Q=0\)
\[
\Delta \mathrm{E}=\mathrm{W}
\]
(c) For isothermal process, \(\Delta \mathrm{T}=0\) and
\[
\begin{aligned}
\Delta \mathrm{E} &=0 \\
\mathrm{Q} &=-\mathrm{W}
\end{aligned}
\]
(d) For cyclic process, state functions like
\[
\begin{aligned}
\Delta \mathrm{E} &=0 \\
\mathrm{Q} &=-W
\end{aligned}
\]

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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