A system absorb `600 J` of heat and work equivalent to `300 J` on its surroundings. The change in internal energy

Options

A. 300 J
B. 400 J
C. 500 J
D. 600 J

Answer

To solve the problem, 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 on the surroundings.

### Step-by-Step Solution:

1. **Identify the Heat Absorbed**:
The system absorbs \(600 \, J\) of heat. According to the convention, when heat is absorbed by the system, it is considered positive.
\[ Q = +600 \, J \]

2. **Identify the Work Done**:
The problem states that the system does work equivalent to \(300 \, J\) on its surroundings. When work is done by the system, it is considered negative in the context of the first law of thermodynamics.
\[ W = -300 \, J \]

3. **Apply the First Law of Thermodynamics**:
Substitute the values of \(Q\) and \(W\) into the equation:
\[ \Delta U = Q - W \]
\[ \Delta U = 600 \, J - (-300 \, J) \]

4. **Simplify the Equation**:
Since subtracting a negative is the same as adding, we can rewrite the equation:
\[ \Delta U = 600 \, J + 300 \, J \]
\[ \Delta U = 900 \, J \]

5. **Final Result**:
The change in internal energy of the system is:
\[ \Delta U = 900 \, J \]

### Summary:
The change in internal energy of the system is \(900 \, J\).

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