For an ideal gas,
(i) the change in internal energy 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 heat capacity at constant volume and `n` is the number of moles of the gas
(ii) The change in internal enregy of the gas and the work done by the gas are equal in magnitude in an adiabatic process.
(iii) The internal energy does not change in an isothermal process. ltbr. (iv) no heat is added or removed in an adiabatic process

Options

A. (i),(iii)
B. (ii),(iii)
C. (iii),(iv)
D. all

Answer

To analyze the statements regarding the behavior of an ideal gas, we will evaluate each statement step by step.

### Step 1: Evaluate Statement (i)
The statement claims that the change in internal energy 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 heat capacity at constant volume and \(n\) is the number of moles of the gas.

**Analysis:**
- For an ideal gas, the internal energy \(U\) is a function of temperature only, and it can be expressed as:
\[ \Delta U = nC_V(T_2 - T_1) \]
- This equation is valid for any process, including constant pressure, because \(C_V\) is used for internal energy changes. Therefore, this statement is **incorrect** as it should be \(nC_V(T_2 - T_1)\) for constant volume, not constant pressure.

### Step 2: Evaluate Statement (ii)
The second statement asserts that 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 (\(Q = 0\)). According to the first law of thermodynamics:
\[ \Delta U = Q - W \]
- Since \(Q = 0\), we have:
\[ \Delta U = -W \]
- 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 **incorrect**.

### Step 3: Evaluate Statement (iii)
The third statement claims that the internal energy does not change in an isothermal process.

**Analysis:**
- In an isothermal process, the temperature remains constant. Since the internal energy of an ideal gas is a function of temperature, if the temperature does not change, the internal energy also does not change.
- Therefore, this statement is **correct**.

### Step 4: Evaluate Statement (iv)
The fourth statement states that no heat is added or removed in an adiabatic process.

**Analysis:**
- By definition, an adiabatic process is one in which no heat is exchanged with the surroundings. Therefore, this statement is **correct**.

### Conclusion
After evaluating all statements:
- Statement (i): Incorrect
- Statement (ii): Incorrect
- Statement (iii): Correct
- Statement (iv): Correct

Thus, the correct statements are (iii) and (iv).

### Final Answer
The correct statements are (iii) and (iv).

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