When a gas is supplied 'dQ' heat, it performs a work 'dW' . The increase in its internal energy 'dU' is

Options

A. dU=dQ+dW
B. dU=dQ-dW
C. dU=dW-dQ
D. `dU=(dQ-dW)/2`

Answer

To solve the problem, we can use the First Law of Thermodynamics, which states:

\[ dQ = dU + dW \]

Where:
- \(dQ\) is the heat added to the system,
- \(dU\) is the change in internal energy of the system,
- \(dW\) is the work done by the system.

### Step-by-Step Solution:

1. **Understanding the First Law of Thermodynamics**:
The First Law of Thermodynamics relates the heat added to a system, the change in internal energy, and the work done by the system. It can be expressed mathematically as:
\[ dQ = dU + dW \]

2. **Rearranging the Equation**:
To find the change in internal energy \(dU\), we can rearrange the equation:
\[ dU = dQ - dW \]

3. **Substituting Known Values**:
In the context of the question, we know the values of \(dQ\) (the heat supplied to the gas) and \(dW\) (the work done by the gas). We can substitute these values into the rearranged equation:
\[ dU = dQ - dW \]

4. **Conclusion**:
The increase in internal energy \(dU\) is equal to the heat supplied \(dQ\) minus the work done \(dW\) by the gas. Therefore, the final expression for the increase in internal energy is:
\[ dU = dQ - dW \]

### Final Answer:
The increase in internal energy \(dU\) is given by:
\[ dU = dQ - dW \]