`DeltaU+DeltaW=0`is valid for

Options

A. Adiabatic process
B. Isochoric process
C. Isobaric process
D. Isothermal process

Answer

To solve the question, we need to analyze the equation \(\Delta U + \Delta W = 0\) and determine for which thermodynamic process this equation holds true.

### Step-by-Step Solution:

1. **Understanding the Equation**:
The equation \(\Delta U + \Delta W = 0\) implies that the change in internal energy (\(\Delta U\)) plus the work done (\(\Delta W\)) is zero. This can be rearranged to show that:
\[ \Delta U = -\Delta W \]

2. **Applying the First Law of Thermodynamics**:
According to the first law of thermodynamics, we have:
\[ \Delta Q = \Delta U + \Delta W \]
where \(\Delta Q\) is the heat added to the system.

3. **Substituting into the First Law**:
If we substitute \(\Delta U + \Delta W = 0\) into the first law, we get:
\[ \Delta Q = 0 \]
This indicates that there is no net heat transfer into or out of the system.

4. **Identifying the Process**:
A process where there is no heat transfer (\(\Delta Q = 0\)) is known as an **adiabatic process**. In an adiabatic process, the system is perfectly insulated, meaning that it does not exchange heat with its surroundings.

5. **Conclusion**:
Therefore, the equation \(\Delta U + \Delta W = 0\) is valid for an **adiabatic process**.

### Final Answer:
The equation \(\Delta U + \Delta W = 0\) is valid for an **adiabatic process**.