If 150 J of heat is added to a system and the work done by the system is 110 j. then change in internal energy wil be

Options

A. 260 J
B. 150 J
C. 110 J
D. 40 J

Answer

To solve the problem, we will use the first law of thermodynamics, which states that the change in internal energy (ΔU) of a system is equal to the heat added to the system (ΔQ) minus the work done by the system (ΔW).

### Step-by-Step Solution:

1. **Identify the Given Values**:
- Heat added to the system (ΔQ) = 150 J
- Work done by the system (ΔW) = 110 J

2. **Understand the Sign Convention**:
- When work is done by the system, it is considered negative in the equation. Therefore, we will take ΔW as -110 J.

3. **Apply the First Law of Thermodynamics**:
The first law of thermodynamics can be expressed as:
\[ \Delta U = \Delta Q - \Delta W \]

4. **Substitute the Values into the Equation**:
\[ \Delta U = 150 J - (-110 J) \]
Since ΔW is negative, subtracting a negative is the same as adding:
\[ \Delta U = 150 J + 110 J \]

5. **Calculate the Change in Internal Energy**:
\[ \Delta U = 260 J \]

### Final Answer:
The change in internal energy (ΔU) is **260 J**.