A system releases 100 kJ of heat while 80 kJ of work is done on the system. Calculate the change in internal energy.

Answer

To solve the problem of calculating the change 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:
- \(\Delta U\) = Change in internal energy
- \(Q\) = Heat added to the system (positive if added, negative if released)
- \(W\) = Work done on the system (positive if done on the system, negative if done by the system)

### Step-by-Step Solution:

1. **Identify the values given in the problem**:
- Heat released by the system, \(Q = -100 \, \text{kJ}\) (since the system releases heat, it is negative).
- Work done on the system, \(W = +80 \, \text{kJ}\) (since work is done on the system, it is positive).

2. **Substitute the values into the first law of thermodynamics**:
\[ \Delta U = Q + W \]
Plugging in the values:
\[ \Delta U = -100 \, \text{kJ} + 80 \, \text{kJ} \]

3. **Perform the calculation**:
\[ \Delta U = -100 + 80 = -20 \, \text{kJ} \]

4. **Conclusion**:
The change in internal energy of the system is:
\[ \Delta U = -20 \, \text{kJ} \]

### Final Answer:
The change in internal energy is \(-20 \, \text{kJ}\).

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