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:

Isothermal means $\Delta U = 0$. Adiabatic means $\Delta Q = 0$.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
An isothermal process happens at constant temperature (\(\Delta T = 0\)). For an ideal gas, internal energy (\(U\)) depends solely on temperature.
Step 2: Key Formula or Approach:
First Law of Thermodynamics: \(Q = \Delta U + W\).
Step 3: Detailed Explanation:
In an isothermal process for an ideal gas:
1. Since \(T = \text{constant}\), the change in internal energy \(\Delta U = n C_v \Delta T = 0\).
2. From the first law: \(Q = 0 + W \implies Q = W\).

This means that any heat (\(Q\)) absorbed by the gas from the surroundings is exactly balanced by the work (\(W\)) done by the gas during its expansion. No energy is stored as internal energy.
Step 4: Final Answer:
The heat is entirely used to do work.