In an adiabatic process 90 J of work is done on the gas. The change in internal energy of the gas is

Options

A. `-90 j`
B. `+90 j`
C. 0 j
D. Depends on initial temperature

Answer

To solve the problem, we need to apply the first law of thermodynamics, which is given by the equation:

\[ \Delta Q = \Delta U + \Delta W \]

Where:
- \(\Delta Q\) is the heat added to the system,
- \(\Delta U\) is the change in internal energy,
- \(\Delta W\) is the work done on the system.

### Step-by-Step Solution:

1. **Identify the type of process**: The problem states that the process is adiabatic. In an adiabatic process, there is no heat exchange with the surroundings, which means:
\[ \Delta Q = 0 \]

2. **Substitute \(\Delta Q\) into the first law of thermodynamics**: Since \(\Delta Q = 0\), we can rewrite the first law of thermodynamics as:
\[ 0 = \Delta U + \Delta W \]

3. **Rearrange the equation**: We can rearrange this equation to solve for the change in internal energy (\(\Delta U\)):
\[ \Delta U = -\Delta W \]

4. **Identify the work done on the gas**: The problem states that 90 J of work is done on the gas. This means:
\[ \Delta W = -90 \, \text{J} \]
(The work done on the gas is considered negative in our equation since it is work done on the system).

5. **Substitute \(\Delta W\) into the equation for \(\Delta U\)**:
\[ \Delta U = -(-90 \, \text{J}) = 90 \, \text{J} \]

6. **Conclusion**: The change in internal energy of the gas is:
\[ \Delta U = 90 \, \text{J} \]

### Final Answer:
The change in internal energy of the gas is **90 J**.

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