Statement-I: it is possible for both the pressure and volume of a monoatomic ideal gas of a given amount to change simultaneously without causing the internal energy of the gas to change.
Statement-2: The internal energy of an ideal gas of a given amount remains constant if temperature does not change. it is possible to have a process in which pressure and volume are changed such that temperature remains constant.

Options

A. Statement-1 is true, Statement-2: is true, Statement-2 is a correct explanation for Statement-1.
B. Statement-1 is true, Statement-2: is true, Statement-2 is NOT a correct explanation for Statement-1.
C. Statement-1 is true but statement-2 is false
D. Statement-1 is false, Statement-2 is true

Explanation

To solve the question, we need to analyze both statements regarding the behavior of a monoatomic ideal gas.

### Step-by-Step Solution:

1. **Understanding Internal Energy**:
- The internal energy (U) of an ideal gas is directly related to its temperature (T). For a monoatomic ideal gas, the internal energy can be expressed as:
\[ U = \frac{3}{2} nRT \]
where \(n\) is the number of moles, \(R\) is the universal gas constant, and \(T\) is the temperature.

2. **Analyzing Statement 1**:
- Statement 1 claims that both pressure (P) and volume (V) can change simultaneously without causing a change in internal energy.
- Since internal energy is a function of temperature only, if the temperature remains constant, then the internal energy will also remain constant.

3. **Analyzing Statement 2**:
- Statement 2 states that the internal energy of an ideal gas remains constant if the temperature does not change. This is true because, as established, internal energy is dependent solely on temperature.
- Furthermore, it is possible to have a process (isothermal process) where both pressure and volume change while keeping the temperature constant. According to the ideal gas law:
\[ PV = nRT \]
If \(T\) is constant, then \(PV\) is also constant, allowing for simultaneous changes in P and V.

4. **Conclusion**:
- Both statements are correct. Statement 2 provides the correct explanation for Statement 1. Hence, it is indeed possible for both pressure and volume of a monoatomic ideal gas to change simultaneously without causing a change in internal energy, provided the temperature remains constant.

### Final Answer:
Both Statement 1 and Statement 2 are correct, and Statement 2 is the correct explanation for Statement 1.

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