When an ideal gas undergoes an adiabatic change causing a temperature change `DeltaT`
(i) there is no heat ganied or lost by the gas
(ii) the work done by the gas is equal to change in internal eenrgy
(iii) the change in internal energy per mole of the gas is `C_(V)DeltaT`, where `C_(V)` is the molar heat capacity at constant volume.

Options

A. (i),(ii),(iii) correct
B. (i),(ii) correct
C. (i),(iii) correct
D. (i)correct

Answer

To solve the problem regarding the adiabatic change of an ideal gas, we will analyze each statement one by one.

### Step 1: Analyze Statement (i)
**Statement (i):** There is no heat gained or lost by the gas.

In an adiabatic process, by definition, there is no heat exchange with the surroundings. This means that the heat transfer \( \Delta Q = 0 \). Therefore, this statement is **correct**.

### Step 2: Analyze Statement (ii)
**Statement (ii):** The work done by the gas is equal to the change in internal energy.

According to the first law of thermodynamics, the relationship is given by:
\[ \Delta Q = \Delta U + W \]
In an adiabatic process, since \( \Delta Q = 0 \), we have:
\[ 0 = \Delta U + W \implies W = -\Delta U \]
This means that the work done by the gas is equal to the negative of the change in internal energy. Therefore, this statement is **incorrect**.

### Step 3: Analyze Statement (iii)
**Statement (iii):** The change in internal energy per mole of the gas is \( C_V \Delta T \), where \( C_V \) is the molar heat capacity at constant volume.

The change in internal energy for an ideal gas is given by:
\[ \Delta U = n C_V \Delta T \]
For one mole of gas (\( n = 1 \)), this simplifies to:
\[ \Delta U = C_V \Delta T \]
Thus, this statement is **correct**.

### Conclusion
Based on the analysis:
- Statement (i) is correct.
- Statement (ii) is incorrect.
- Statement (iii) is correct.

Therefore, the correct options are **(i) and (iii)**.

### Final Answer
The correct statements are: **1 and 3 are correct.**

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