If a gas is comprssed adiabatically by doing work of 150 J the change in internal energy of the gas is

Options

A. 100 J
B. 150 J
C. 200 J
D. 250 J

Explanation

To solve the problem of finding the change in internal energy of a gas compressed adiabatically by doing 150 J of work, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Adiabatic Process**:
In an adiabatic process, there is no heat exchange with the surroundings. This means that the heat transfer \( dq = 0 \).

2. **Applying the First Law of Thermodynamics**:
The first law of thermodynamics states:
\[ \Delta U = Q - W \]
where \( \Delta U \) is the change in internal energy, \( Q \) is the heat added to the system, and \( W \) is the work done by the system.

3. **Substituting Values**:
Since the process is adiabatic, we have \( Q = 0 \). Thus, the equation simplifies to:
\[ \Delta U = 0 - W \]
or
\[ \Delta U = -W \]

4. **Identifying Work Done**:
In this case, work is done on the gas, which means we consider \( W \) as positive when work is done on the system. Given that the work done is 150 J, we have:
\[ W = 150 \, \text{J} \]

5. **Calculating Change in Internal Energy**:
Now substituting the value of \( W \) into the equation:
\[ \Delta U = -150 \, \text{J} \]

6. **Final Result**:
The change in internal energy \( \Delta U \) of the gas is:
\[ \Delta U = 150 \, \text{J} \]

### Final Answer:
The change in internal energy of the gas is **150 J**.