For an ideal gas :

Options

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

Explanation

To solve the question regarding the statements about an ideal gas, we will analyze each statement one by one and determine if they are correct or not.

### Step-by-Step Solution:

1. **Statement 1**: The change in internal energy in a constant pressure process from temperature T1 to T2 is equal to \( nC_v(T_2 - T_1) \).
- **Analysis**: For an ideal gas, the internal energy \( U \) is a function of temperature only. The change in internal energy (\( \Delta U \)) can be expressed as:
\[ \Delta U = nC_v(T_2 - T_1) \]
This is valid regardless of whether the process is at constant pressure or constant volume. Therefore, this statement is **correct**.

2. **Statement 2**: The change in internal energy of the gas and the work done by the gas are equal in magnitude in an adiabatic process.
- **Analysis**: In an adiabatic process, there is no heat exchange (\( \Delta Q = 0 \)). According to the first law of thermodynamics:
\[ \Delta U = Q - W \]
Since \( Q = 0 \), it simplifies to:
\[ \Delta U = -W \]
This means that the change in internal energy is equal in magnitude but opposite in sign to the work done by the gas. Thus, this statement is also **correct**.

3. **Statement 3**: The internal energy does not change in an isothermal process.
- **Analysis**: In an isothermal process, the temperature remains constant (\( T = \text{constant} \)). Since the internal energy of an ideal gas depends only on temperature, if the temperature does not change, the internal energy also does not change. Therefore, this statement is **correct**.

4. **Statement 4**: No heat is added or removed in an adiabatic process.
- **Analysis**: By definition, an adiabatic process is one in which there is no heat transfer between the system and its surroundings. Thus, there is no heat added or removed. Hence, this statement is also **correct**.

### Conclusion:
All four statements regarding the ideal gas are correct.