A system gives out 30 J of heat and does 75 J of work. What is the internal energy change?

Explanation

To find the change in internal energy of the system, we can use the first law of thermodynamics, which states:

\[ \Delta U = Q + W \]

Where:
- \(\Delta U\) is the change in internal energy,
- \(Q\) is the heat exchanged, and
- \(W\) is the work done.

### Step-by-Step Solution:

1. **Identify the Heat Exchange (Q)**:
- The problem states that the system gives out 30 J of heat. When heat is released by the system, it is considered negative.
- Therefore, \(Q = -30 \, \text{J}\).

2. **Identify the Work Done (W)**:
- The problem states that the system does 75 J of work. Work done by the system is also considered negative.
- Therefore, \(W = -75 \, \text{J}\).

3. **Apply the First Law of Thermodynamics**:
- Substitute the values of \(Q\) and \(W\) into the equation:
\[ \Delta U = Q + W = -30 \, \text{J} + (-75 \, \text{J}) \]

4. **Calculate the Change in Internal Energy**:
- Combine the values:
\[ \Delta U = -30 \, \text{J} - 75 \, \text{J} = -105 \, \text{J} \]

5. **Conclusion**:
- The change in internal energy of the system is:
\[ \Delta U = -105 \, \text{J} \]

### Final Answer:
The internal energy change is \(-105 \, \text{J}\).