Calculate the increase in internal energy of system when 40 joule heat is supplied and the work done by a system is 8 joule

Options

A. 25 J
B. 30 J
C. 32 J
D. 28 J

Answer

To calculate the increase in internal energy of the system, we can 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 supplied to the system,
- \(W\) is the work done by the system.

### Step-by-Step Solution:

1. **Identify the given values**:
- Heat supplied, \(Q = 40 \, \text{Joules}\)
- Work done by the system, \(W = 8 \, \text{Joules}\)

2. **Understand the sign convention**:
- According to thermodynamics, when work is done by the system, it is considered negative in the equation. Therefore, we will take:
\[ W = -8 \, \text{Joules} \]

3. **Substitute the values into the equation**:
\[ \Delta U = Q - W \]
Plugging in the values:
\[ \Delta U = 40 \, \text{J} - (-8 \, \text{J}) \]

4. **Simplify the equation**:
\[ \Delta U = 40 \, \text{J} + 8 \, \text{J} = 48 \, \text{J} \]

5. **Conclusion**:
The increase in internal energy of the system is:
\[ \Delta U = 48 \, \text{Joules} \]