What will be the change in internal energy when 12 kJ of work is done on the system and 2 kJ of heat is given by the system?

Options

A. `+10kJ`
B. `-10kJ`
C. `+5kJ`
D. `-5kJ`

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,
- \(W\) is the work done on the system.

### Step-by-Step Solution:

1. **Identify Work Done on the System**:
- It is given that 12 kJ of work is done on the system. According to the convention, when work is done on the system, it is considered positive.
- Therefore, \(W = +12 \, \text{kJ}\).

2. **Identify Heat Given by the System**:
- It is stated that 2 kJ of heat is given by the system. When the system gives off heat, it is losing heat, which is considered negative.
- Therefore, \(Q = -2 \, \text{kJ}\).

3. **Apply the First Law of Thermodynamics**:
- Substitute the values of \(Q\) and \(W\) into the equation:
\[ \Delta U = Q + W = (-2 \, \text{kJ}) + (+12 \, \text{kJ}) \]

4. **Calculate the Change in Internal Energy**:
- Perform the calculation:
\[ \Delta U = -2 + 12 = +10 \, \text{kJ} \]

5. **Conclusion**:
- The change in internal energy of the system is \(+10 \, \text{kJ}\).

### Final Answer:
The change in internal energy is \(+10 \, \text{kJ}\).