When gases are mixed, the internal energy will remain conserved. When external energy provides heat energy there may be temperature variation leading to internal energy change and/or volume variation spending/gaving work/energy. The change is internal energy is independent of the path followed, while work and heat energy depends on the path followed. Internal energy depends on the number of degrees of freedom which in turn affects the ratio of specific heat capacities.
In a process with a temperature change of dT, internal energy changes by `dU = nC_vdT` . The process is applicable for

Options

A. Constant volume
B. Constant pressure
C. Constant energy
D. All of these

Answer

To solve the question regarding the change in internal energy when gases are mixed and the conditions under which the equation \( dU = nC_v dT \) is applicable, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Internal Energy**:
- The internal energy \( U \) of a gas is a function of its temperature and the number of moles. For an ideal gas, the change in internal energy can be expressed as:
\[ dU = nC_v dT \]
- Here, \( n \) is the number of moles, \( C_v \) is the molar specific heat capacity at constant volume, and \( dT \) is the change in temperature.

2. **Identifying the Process**:
- The equation \( dU = nC_v dT \) is specifically applicable when the process occurs at constant volume. This means that there is no change in volume (\( dV = 0 \)) during the process.

3. **Applying the First Law of Thermodynamics**:
- According to the first law of thermodynamics:
\[ dU = dQ - dW \]
- In a constant volume process, the work done \( dW \) is zero because:
\[ dW = P dV = 0 \]
- Therefore, we can rewrite the first law as:
\[ dU = dQ \]

4. **Relating Heat Transfer to Internal Energy Change**:
- Since \( dQ \) at constant volume is given by:
\[ dQ = nC_v dT \]
- We can substitute this into our first law equation:
\[ dU = nC_v dT \]
- This confirms that the change in internal energy is equal to the heat added to the system at constant volume.

5. **Conclusion**:
- Thus, the process described by the equation \( dU = nC_v dT \) is applicable for a constant volume process.

### Final Answer:
The process is applicable for a constant volume process.