If pressure of an ideal gas is doubled and volume is halved, then its internal energy will remain unchanged.
Internal energy of an ideal gas is a function of only temperature.

Options

A. If both Assertion and Reason are true and the reason is correct explanation of the Assertion.
B. If both Assertion and Reason are true but Reason is not the correct explanation of Assertion.
C. If Assertion is true, but the Reason is false.
D. If Assertion is false but the Reason is true.

Explanation

To solve the question, we need to analyze the assertion and the reason given in the statement.

### Step-by-Step Solution:

1. **Understanding the Assertion**:
The assertion states that if the pressure of an ideal gas is doubled and the volume is halved, then its internal energy will remain unchanged.

2. **Using the Ideal Gas Law**:
The ideal gas law is given by the equation:
\[ PV = nRT \]
Where \( P \) is pressure, \( V \) is volume, \( n \) is the number of moles, \( R \) is the gas constant, and \( T \) is temperature.

3. **Applying the Changes**:
According to the assertion, the pressure \( P \) is doubled (\( P' = 2P \)) and the volume \( V \) is halved (\( V' = \frac{V}{2} \)). We can substitute these values into the ideal gas law:
\[ P'V' = (2P) \left(\frac{V}{2}\right) = PV \]
This shows that the product \( PV \) remains constant, indicating that the temperature \( T \) must also remain constant.

4. **Internal Energy and Temperature**:
The internal energy \( U \) of an ideal gas is a function of temperature only. For an ideal gas, the internal energy can be expressed as:
\[ U = nC_VT \]
Where \( C_V \) is the molar heat capacity at constant volume. Since the temperature \( T \) remains unchanged (as shown in the previous step), the internal energy \( U \) will also remain unchanged.

5. **Conclusion**:
Therefore, the assertion is true because the internal energy does not change when the temperature remains constant.

6. **Analyzing the Reason**:
The reason states that the internal energy of an ideal gas is a function of only temperature, which is also true. However, it does not directly explain why the internal energy remains unchanged when pressure and volume change.

7. **Final Evaluation**:
Both the assertion and reason are true, but the reason does not provide a correct explanation for the assertion. Therefore, the correct choice is that both assertion and reason are true, but the reason is not the correct explanation for the assertion.

### Final Answer:
Both assertion and reason are true, but the reason is not the correct explanation for the assertion.

---