Question

A monoatomic gas of \( n \)-moles is heated from temperature \( T_1 \) to \( T_2 \) under two different conditions:

• A. More when heated at constant volume
• B. More when heated at constant pressure
• C. Same in both the cases
• D. Zero in both the cases

Hint:

The internal energy of an ideal gas depends only on temperature. It remains the same for a given temperature change, regardless of whether the process is at constant volume or constant pressure.

Answer 1

The Correct Option is C

Step 1: Understanding Internal Energy Change 
For an ideal gas, the internal energy \( U \) depends only on temperature and is given by: \[ \Delta U = n C_V \Delta T. \] Since internal energy is a state function, the change in internal energy depends only on the initial and final temperatures, regardless of the process. 
Step 2: Applying to Both Conditions 
- When heated at constant volume: \[ \Delta U = n C_V (T_2 - T_1). \] - When heated at constant pressure: \[ \Delta U = n C_V (T_2 - T_1). \] Since \( \Delta U \) depends only on \( T_2 - T_1 \), it is the same in both cases. 
Step 3: Conclusion 
Thus, the change in internal energy remains the same whether heating occurs at constant volume or constant pressure.