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

Options

A. Decrease by 6 kJ
B. Increase by 6 kJ
C. Decrease by 14 kJ
D. Increase by 14 kJ

Answer

To find the internal energy of the system, we will 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:

**Step 1: Identify the heat absorbed by the system.**
- The system absorbs \(10 \, \text{kJ}\) of heat.
- Since heat is absorbed, it is considered positive:
\[ Q = +10 \, \text{kJ} \]

**Step 2: Identify the work done by the system.**
- The system does \(4 \, \text{kJ}\) of work.
- Since the work is done by the system, it is considered negative:
\[ W = -4 \, \text{kJ} \]

**Step 3: Apply the first law of thermodynamics.**
- Substitute the values of \(Q\) and \(W\) into the equation:
\[ \Delta U = Q + W \]
\[ \Delta U = (+10 \, \text{kJ}) + (-4 \, \text{kJ}) \]

**Step 4: Perform the calculation.**
- Combine the values:
\[ \Delta U = 10 \, \text{kJ} - 4 \, \text{kJ} = 6 \, \text{kJ} \]

**Step 5: Interpret the result.**
- The change in internal energy \(\Delta U\) is \(+6 \, \text{kJ}\), which indicates that the internal energy of the system has increased by \(6 \, \text{kJ}\).

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

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