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

Options

A. decreases
B. increases
C. same
D. none

Explanation

To solve the problem, we will use the first law of thermodynamics, which states that the change in internal energy (ΔU) of a system is equal to the heat added to the system (Q) plus the work done on the system (W). The formula can be expressed as:

\[ \Delta U = Q + W \]

### Step-by-Step Solution:

1. **Identify the given values:**
- Heat absorbed by the system (Q) = +10 kJ (since the system absorbs heat, it is positive)
- Work done by the system (W) = -4 kJ (since the system does work, it is considered negative)

2. **Substitute the values into the first law of thermodynamics:**
\[ \Delta U = Q + W \]
\[ \Delta U = 10 \, \text{kJ} + (-4 \, \text{kJ}) \]

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

4. **Interpret the result:**
- Since ΔU is positive (+6 kJ), it indicates that the internal energy of the system is increasing.

### Final Answer:
The internal energy of the system increases by 6 kJ.

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