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

Options

A. a. 100 J
B. b. 150 J
C. c. 200 J
D. d. 250 J

Explanation

To find the change in internal energy of a gas that is compressed adiabatically by doing work of 150 J, we can follow these steps:

### Step 1: Understand the Process
In an adiabatic process, there is no heat exchange with the surroundings. The work done on the gas will affect its internal energy.

### Step 2: Identify the Work Done
The problem states that the gas is compressed, which means work is done on the gas. The work done is given as 150 J. However, since the gas is being compressed, we consider the work done on the gas as negative. Therefore, we can write:
\[ dW = -150 \, \text{J} \]

### Step 3: Use the First Law of Thermodynamics
The first law of thermodynamics states:
\[ dU = dQ + dW \]
For an adiabatic process, \( dQ = 0 \) (no heat exchange). Therefore, the equation simplifies to:
\[ dU = dW \]

### Step 4: Substitute the Work Done
Now, substituting the value of \( dW \):
\[ dU = -150 \, \text{J} \]

### Step 5: Calculate the Change in Internal Energy
Since we have established that \( dU = dW \) in an adiabatic process, we can conclude:
\[ dU = -(-150 \, \text{J}) = 150 \, \text{J} \]

### Conclusion
The change in internal energy of the gas is:
\[ \Delta U = 150 \, \text{J} \]

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

---