In above question, if `U_(a) = 40J`, value of `U_(b)` will be

Options

A. `-50 J`
B. `100 J`
C. `-120 J`
D. `160 J`

Explanation

To find the value of \( U_b \) given that \( U_a = 40 \, J \) and the change in internal energy \( \Delta U \) from state A to state B is \( 120 \, J \), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the relationship between internal energies**:
The change in internal energy (\( \Delta U \)) between two states is given by:
\[ \Delta U = U_b - U_a \]
where \( U_b \) is the internal energy at state B and \( U_a \) is the internal energy at state A.

2. **Substitute the known values**:
We know that \( U_a = 40 \, J \) and \( \Delta U = 120 \, J \). Therefore, we can rewrite the equation as:
\[ 120 \, J = U_b - 40 \, J \]

3. **Solve for \( U_b \)**:
Rearranging the equation to solve for \( U_b \):
\[ U_b = 120 \, J + 40 \, J \]
\[ U_b = 160 \, J \]

### Final Answer:
Thus, the value of \( U_b \) is \( 160 \, J \).

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