Question

In an isothermal expansion of an ideal gas, the heat supplied to the gas is:

• A. entirely used to increase internal energy
• B. entirely used to do work
• C. partly used to do work and partly to increase internal energy
• D. none of the above

Hint:

For an ideal gas: \[ \Delta U = 0 \] whenever temperature remains constant. Hence, in isothermal expansion, all supplied heat is used to perform work.

Answer 1

The Correct Option is B

Concept: According to the First Law of Thermodynamics: \[ \Delta U = q - w \] For an ideal gas, internal energy depends only on temperature.

Step 1: Understanding the meaning of isothermal process.
In an isothermal process: \[ T = \text{constant} \] Therefore, \[ \Delta T = 0 \]

Step 2: Relating temperature to internal energy.
For an ideal gas: \[ \Delta U \propto \Delta T \] Since \(\Delta T = 0\): \[ \Delta U = 0 \]

Step 3: Applying First Law of Thermodynamics.
\[ \Delta U = q - w \] Substituting \(\Delta U = 0\): \[ 0 = q - w \] \[ q = w \] This means the entire heat supplied is converted into work done by the gas.