A system absorbs 10 kJ of heat and does 4 kJ of work. The internal energy of the system

Options

A. increases by 6 kJ
B. decreases by 6 kJ
C. decreases by 14 kJ
D. increases by 14 kJ

Answer

To find the 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 absorbed by the system,
- \(W\) is the work done by the system.

### Step-by-step solution:

1. **Identify the given values:**
- Heat absorbed by the system, \(Q = 10 \, \text{kJ}\) (since heat is absorbed, it is positive).
- Work done by the system, \(W = 4 \, \text{kJ}\) (since work is done by the system, it is negative in the equation).

2. **Substitute the values into the equation:**
\[ \Delta U = Q - W \]
\[ \Delta U = 10 \, \text{kJ} - 4 \, \text{kJ} \]

3. **Calculate the change in internal energy:**
\[ \Delta U = 10 \, \text{kJ} - 4 \, \text{kJ} = 6 \, \text{kJ} \]

4. **Conclusion:**
The internal energy of the system increases by \(6 \, \text{kJ}\).

### Final Answer:
The internal energy of the system is \(6 \, \text{kJ}\).

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