Change in internal energy of an ideal gas is given by `DeltaU=nC_(V)DeltaT`. This is applicable for (`C_(V)`=molar heat capacity at constant volume)

Options

A. A) isochoric process only
B. B) all processes
C. C) a process where `DeltaT` is positive
D. D) all the processes except isothermal process

Answer

To solve the question regarding the applicability of the equation for the change in internal energy of an ideal gas, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Equation**: The equation given is \(\Delta U = n C_V \Delta T\), where:
- \(\Delta U\) is the change in internal energy.
- \(n\) is the number of moles of the gas.
- \(C_V\) is the molar heat capacity at constant volume.
- \(\Delta T\) is the change in temperature.

2. **Identify the Conditions**: The equation is applicable under certain thermodynamic processes. We need to identify which processes allow for this equation to hold true.

3. **Consider Different Processes**:
- **Adiabatic Process**: In an adiabatic process, there is no heat exchange with the surroundings. The equation is applicable here because the internal energy change is related to the work done on or by the gas.
- **Isothermal Process**: In an isothermal process, the temperature remains constant. However, since \(\Delta T = 0\), the change in internal energy \(\Delta U\) will also be zero, but the equation still holds as it simplifies to \(0 = n C_V \cdot 0\).
- **Isobaric Process**: In an isobaric process, the pressure remains constant. The equation is still applicable since the internal energy can change with temperature.
- **Isochoric Process**: In an isochoric process, the volume remains constant, and the equation directly applies since there is no work done and the internal energy change is solely due to temperature change.

4. **Conclusion**: The equation \(\Delta U = n C_V \Delta T\) is applicable in:
- Adiabatic processes
- Isothermal processes (with \(\Delta T = 0\))
- Isobaric processes
- Isochoric processes

### Final Answer:
The equation \(\Delta U = n C_V \Delta T\) is applicable for adiabatic, isothermal, isobaric, and isochoric processes.

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