For a gaseous state if heat supplied to the system is 100 J and work done by the system is 25 J. then internal energy of the system is

Options

A. 125 J
B. 100 J
C. 50 J
D. 75 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 of the system,
- \(Q\) is the heat supplied to the system,
- \(W\) is the work done by the system.

### Step-by-Step Solution:

1. **Identify the values given in the problem:**
- Heat supplied to the system, \(Q = 100 \, \text{J}\)
- Work done by the system, \(W = 25 \, \text{J}\)

2. **Apply the first law of thermodynamics:**
- According to the first law, we can express the change in internal energy as:
\[ \Delta U = Q - W \]

3. **Substitute the known values into the equation:**
\[ \Delta U = 100 \, \text{J} - 25 \, \text{J} \]

4. **Perform the subtraction:**
\[ \Delta U = 75 \, \text{J} \]

5. **Conclusion:**
- The internal energy of the system is \(75 \, \text{J}\).

### Final Answer:
The internal energy of the system is \(75 \, \text{J}\).

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