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

Answer

To solve the question regarding the change in internal energy of an ideal gas, we will analyze the equation given and the conditions under which it applies.

### Step 1: Understand the Equation
The equation provided 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.

### Step 2: Identify the Conditions for the Equation
This equation is specifically applicable under certain conditions:
- The process must occur at constant volume (isochoric process). In this case, no work is done by the gas, and all the heat added goes into changing the internal energy.
- The equation can also be used in other processes, but the interpretation of \(\Delta U\) may vary.

### Step 3: Analyze Different Processes
1. **Isochoric Process**: Here, the volume remains constant, and thus \(\Delta U = n C_V \Delta T\) directly applies.
2. **Adiabatic Process**: In an adiabatic process, no heat is exchanged with the surroundings. The change in internal energy can still be calculated using the equation, provided you know the change in temperature.
3. **Isobaric Process**: In an isobaric process (constant pressure), the equation does not directly apply because the heat added does not only change the internal energy but also does work on the surroundings.
4. **Isotropic Process**: In an isotropic process, where temperature is constant, \(\Delta T = 0\), thus \(\Delta U = 0\). This means there is no change in internal energy.

### Step 4: Conclusion
The equation \(\Delta U = n C_V \Delta T\) is primarily applicable in an isochoric process. It can also be used in adiabatic processes, but the interpretation may vary. In isotropic processes, the change in internal energy is zero.