The work done by the system is `8` joule, when `40` joule heat is supplied to it. What is the increases in internal energy of system.

Explanation

To find the increase in internal energy of the system, we can use the first law of thermodynamics, which 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.

### Step-by-step Solution:

1. **Identify the values given in the problem:**
- Heat supplied to the system, \(Q = 40 \, \text{joules}\)
- Work done by the system, \(W = 8 \, \text{joules}\)

2. **Substitute the values into the first law of thermodynamics equation:**
\[ \Delta U = Q - W \]
Here, since the work is done by the system, we take it as positive in the equation.

3. **Plug in the values:**
\[ \Delta U = 40 \, \text{joules} - 8 \, \text{joules} \]

4. **Calculate the change in internal energy:**
\[ \Delta U = 40 - 8 = 32 \, \text{joules} \]

5. **Conclusion:**
The increase in internal energy of the system is \(32 \, \text{joules}\).

### Final Answer:
The increase in internal energy of the system is \(32 \, \text{joules}\).

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