For an ideal gas :

Options

A. A) the change in internal energy in a constant pressure process from temperature `T_(1)` and `T_(2)` is equal to `nC_(V)(T_(2)-T_(1))`, where `C_(V)` is the number of moles of the gas
B. B) the change in internal energy of the gas and the work done by the gas are equal in magnitude in an adiabatic process
C. C) the internal energy does not change in an isothermal process
D. D) no heat is added or removed in an adiabatic process

Answer

To solve the question regarding the properties of an ideal gas, we need to analyze each of the given options based on our understanding of thermodynamics and the behavior of ideal gases.

### Step-by-Step Solution:

1. **Understanding Internal Energy Change**:
For an ideal gas, the change in internal energy (ΔU) is given by the formula:
\[ \Delta U = nC_V \Delta T \]
where \(n\) is the number of moles, \(C_V\) is the specific heat at constant volume, and \(\Delta T\) is the change in temperature.

**Hint**: Remember that internal energy is related to temperature change for an ideal gas.

2. **Analyzing the Adiabatic Process**:
In an adiabatic process, there is no heat exchange with the surroundings, which means:
\[ Q = 0 \]
According to the first law of thermodynamics:
\[ \Delta U = Q - W \]
Since \(Q = 0\), we have:
\[ \Delta U = -W \]
This means the change in internal energy is equal in magnitude but opposite in sign to the work done by the gas.

**Hint**: In an adiabatic process, focus on the relationship between internal energy and work done.

3. **Isothermal Process Analysis**:
In an isothermal process, the temperature remains constant (\(\Delta T = 0\)). Therefore, the change in internal energy is:
\[ \Delta U = nC_V \cdot 0 = 0 \]
This indicates that there is no change in internal energy during an isothermal process.

**Hint**: For isothermal processes, remember that temperature does not change, leading to no change in internal energy.

4. **Evaluating Each Option**:
- **Option A**: Correct. The change in internal energy at constant pressure is given by \(nC_P \Delta T\), but the statement is generally true for internal energy change.
- **Option B**: Correct. In an adiabatic process, the change in internal energy is equal in magnitude to the work done by the gas.
- **Option C**: Correct. In an isothermal process, the change in internal energy is zero.
- **Option D**: Correct. In an adiabatic process, no heat is added or removed.

5. **Conclusion**:
All options (A, B, C, D) are correct regarding the behavior of an ideal gas under different thermodynamic processes.

**Final Answer**: All options are correct.