calculate the change in internal energy of a gas kept in a rigid container when 100 J of heat is supplied to it.

Explanation

To calculate the change in internal energy of a gas kept in a rigid container when 100 J of heat is supplied to it, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the System**: We have a gas in a rigid container. A rigid container means that the volume of the gas does not change. Therefore, the volume is constant.

2. **Identify Given Values**: We are given that the heat supplied to the system (the gas) is \( Q = 100 \, \text{J} \).

3. **Apply the First Law of Thermodynamics**: The first law of thermodynamics is given by the equation:
\[ \Delta U = Q - W \]
where:
- \( \Delta U \) is the change in internal energy,
- \( Q \) is the heat added to the system,
- \( W \) is the work done by the system.

4. **Determine Work Done**: Since the container is rigid, there is no change in volume (\( \Delta V = 0 \)). The work done by the gas is given by:
\[ W = P \Delta V \]
Since \( \Delta V = 0 \), we have:
\[ W = 0 \]

5. **Calculate Change in Internal Energy**: Substituting the values into the first law equation:
\[ \Delta U = Q - W \]
\[ \Delta U = 100 \, \text{J} - 0 \]
\[ \Delta U = 100 \, \text{J} \]

Thus, the change in internal energy of the gas is \( 100 \, \text{J} \).

### Summary:
The change in internal energy of the gas when 100 J of heat is supplied to it in a rigid container is \( 100 \, \text{J} \).