In thermodynamic process, 200 Joules of heat is given to a gas and 100 Joules of work is also done on it. The change in internal energy of the gas is

Options

A. `100j`
B. `300j`
C. `419j`
D. `24j`

Answer

To find the change in internal energy of the gas, we can use the first law of thermodynamics, which states:

\[ \Delta U = Q - W \]

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

### Step-by-Step Solution:

1. **Identify the heat added to the gas**:
- The problem states that 200 Joules of heat is given to the gas. Since heat is added to the system, we take this as positive.
\[ Q = +200 \, \text{Joules} \]

2. **Identify the work done on the gas**:
- The problem states that 100 Joules of work is done on the gas. When work is done on the system, it is considered negative in the context of the first law of thermodynamics.
\[ W = -100 \, \text{Joules} \]

3. **Apply the first law of thermodynamics**:
- Substitute the values of \(Q\) and \(W\) into the equation:
\[ \Delta U = Q - W \]
\[ \Delta U = 200 - (-100) \]

4. **Simplify the equation**:
- This simplifies to:
\[ \Delta U = 200 + 100 = 300 \, \text{Joules} \]

5. **Conclusion**:
- The change in internal energy of the gas is:
\[ \Delta U = 300 \, \text{Joules} \]

### Final Answer:
The change in internal energy of the gas is **300 Joules**.

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