Question

A gas goes through: (i) isothermal expansion \( W = 50J \), (ii) adiabatic \( W = ? \), (iii) isothermal expansion \( W = 20J \). Total \( \Delta U = -30J \). Find work in adiabatic.

• A. 40 J
• B. 100 J
• C. 30 J
• D. 20 J

Hint:

In cyclic processes, apply energy conservation across all paths. \( \Delta U = Q - W \)

Answer 1

The Correct Option is A

From First Law: \[ \Delta U = Q - W \Rightarrow \Delta U = (Q_1 + Q_2 + Q_3) - (W_1 + W_2 + W_3) \] For isothermal: \( \Delta U = 0 \), so \( Q = W \) Given: \[ W_1 = 50, W_3 = 20, W_2 = ?, \quad \Delta U = -30 = Q - (50 + W_2 + 20) \Rightarrow Q = 70 + W_2 \] Also \( Q = W_1 + W_3 = 70 \), so \[ -30 = 70 - (70 + W_2) \Rightarrow W_2 = 40\ \text{J} \]