Question

A system undergoes isothermal reversible expansion. What is true about the work done by the system?

• A. It is less than the heat absorbed.
• B. It equals the heat absorbed.
• C. It is more than the heat absorbed.
• D. No work is done.

Hint:

Isothermal Process (Ideal Gas). Temperature is constant (\(\Delta T = 0\)). Internal energy change is zero (\(\Delta U = 0\)). First Law becomes \(Q = W\). Heat absorbed equals work done by the system during reversible expansion.

Answer 1

The Correct Option is B

Consider the first law of thermodynamics: $$ \Delta U = Q - W $$ where \(\Delta U\) is the change in internal energy, \(Q\) is the heat added to the system, and \(W\) is the work done *by* the system.
The process is isothermal, meaning the temperature (T) is constant.
For an ideal gas (often assumed in such problems unless stated otherwise), the internal energy (\(U\)) depends only on temperature.
Since T is constant, the change in internal energy is zero: $$ \Delta U = 0 $$ Substituting this into the first law: $$ 0 = Q - W $$ $$ Q = W $$ This means that for an isothermal reversible expansion (or compression) of an ideal gas, the work done by the system exactly equals the heat absorbed by the system.
The system absorbs heat from the surroundings to maintain its temperature while doing work during expansion.