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 (ΔU) of a gaseous system when heat is supplied and work is done, 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 given values**:
- Heat supplied to the system, \( Q = 100 \, \text{J} \)
- Work done by the system, \( W = 80 \, \text{J} \)

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

3. **Substitute the known values into the equation**:
- Substitute \( Q = 100 \, \text{J} \) and \( W = 80 \, \text{J} \):
\[ \Delta U = 100 \, \text{J} - 80 \, \text{J} \]

4. **Calculate the change in internal energy**:
- Perform the subtraction:
\[ \Delta U = 20 \, \text{J} \]

5. **Conclusion**:
- The change in internal energy of the gaseous system is \( \Delta U = 20 \, \text{J} \).