A gas of volume changes 2 litre to 10 litre at constant temperature 300K, then the change in internal energy will be :

Options

A. 12 J
B. 24 J
C. 36 J
D. 0 J

Explanation

To solve the problem, we need to analyze the situation described:

1. **Understanding the Problem**: We have a gas that undergoes a volume change from 2 liters to 10 liters at a constant temperature of 300 K. We need to find the change in internal energy (ΔU) of the gas during this process.

2. **Key Concept**: The internal energy of an ideal gas is primarily a function of its temperature. For an ideal gas, the change in internal energy (ΔU) can be expressed as:
\[ \Delta U = n C_v \Delta T \]
where:
- \( n \) is the number of moles of the gas,
- \( C_v \) is the molar heat capacity at constant volume,
- \( \Delta T \) is the change in temperature.

3. **Constant Temperature Condition**: Since the problem states that the process occurs at constant temperature (isothermal process), we have:
\[ \Delta T = 0 \]
This means there is no change in temperature.

4. **Calculating Change in Internal Energy**: Substituting \( \Delta T = 0 \) into the equation for change in internal energy:
\[ \Delta U = n C_v \cdot 0 = 0 \]
Therefore, the change in internal energy (ΔU) is zero.

5. **Conclusion**: The change in internal energy when the gas expands from 2 liters to 10 liters at constant temperature is:
\[ \Delta U = 0 \text{ joules} \]

Thus, the correct answer is option D: 0 joules.