Find the change in internal energy if heat supplied to the gaseous system is 100 J and work done by the system is 80 J.

Options

A. 5 J
B. 30 J
C. 10 J
D. 20 J

Answer

To find the change in internal energy of the gaseous system, we can use the first law of thermodynamics, which is expressed as:

\[ \Delta U = Q - W \]

Where:
- \(\Delta U\) is the change in internal energy,
- \(Q\) 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, \(W = 80 \, \text{J}\)

2. **Substitute the values into the first law of thermodynamics equation:**
\[ \Delta U = Q - W \]
\[ \Delta U = 100 \, \text{J} - 80 \, \text{J} \]

3. **Perform the calculation:**
\[ \Delta U = 20 \, \text{J} \]

4. **Conclusion:**
The change in internal energy of the gaseous system is \(20 \, \text{J}\).

### Final Answer:
\[ \Delta U = 20 \, \text{J} \]