MHT CET · Physics · Thermodynamics

In a thermodynamic system ' \(\Delta \mathrm{U}\) ' represents the increase in internal energy and 'W' the work done by the system. Which of the following statement is true?

A \(\Delta \mathrm{U}=-\mathrm{W}\) in an adiabatic process.
B \(\Delta \mathrm{U}=\mathrm{W}\) in an isothermal process.
C \(\Delta \mathrm{U}=-\mathrm{W}\) in an isothermal process.
D \(\Delta U=W\) in an adiabatic process.

Verified Solution

Answer & Solution

Correct Answer

(A) \(\Delta \mathrm{U}=-\mathrm{W}\) in an adiabatic process.

Step-by-step Solution

Detailed explanation

For an isothermal process, \(\Delta \mathrm{U}=0\). According to first law of thermodynamics, \(\Delta \mathrm{Q}=\Delta \mathrm{U}+\mathrm{W}\)
For an adiabatic process,
\(\begin{array}{rlrl}
& & \Delta \mathrm{Q} & =0 \\
\therefore \quad & \Delta \mathrm{U} & =-\mathrm{W}
\end{array}\)

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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