One mole of a gas absorbs 200 J of heat at constant volume. Its temperature rises from 298 K to 308 K. The change in internal energy is :-

Explanation

To solve the problem step-by-step, we will use the principles of thermodynamics, specifically focusing on the relationship between heat, work, and internal energy.

### Step-by-Step Solution:

1. **Identify the Given Information:**
- Heat absorbed (Q) = 200 J
- Initial temperature (T1) = 298 K
- Final temperature (T2) = 308 K
- Number of moles (n) = 1 mole
- Process is at constant volume.

2. **Understand the First Law of Thermodynamics:**
The first law of thermodynamics states that:
\[ \Delta U = Q - W \]
where:
- \(\Delta U\) = change in internal energy
- \(Q\) = heat added to the system
- \(W\) = work done by the system

3. **Calculate Work Done (W):**
Since the process occurs at constant volume, there is no change in volume (\(\Delta V = 0\)). Therefore, the work done (W) is given by:
\[ W = P \Delta V = P \times 0 = 0 \]

4. **Substitute Values into the First Law Equation:**
Now, substituting the values into the first law equation:
\[ \Delta U = Q - W \]
Since \(W = 0\):
\[ \Delta U = Q - 0 = Q \]
Thus:
\[ \Delta U = 200 \, \text{J} \]

5. **Conclusion:**
The change in internal energy (\(\Delta U\)) is:
\[ \Delta U = 200 \, \text{J} \]

### Final Answer:
The change in internal energy is **200 J**.