Pick the correct statement(s):

Options

A. The rms translational speed for different ideal gas samples at the same temperature is not necessarily same but it depends on the molar mass
B. Speed of a particular gas molecule can be greater the RMS speed for the sample.
C. Temperature of an ideal gas is doubled from `100^@ C` to `200^@ C`. The average kinetic energy of each particle is also doubled
D. It is possible for both the pressure and volume of a monoatomic ideal gas to change simultaneously without causing the internal energy of the gas to change

Explanation

To determine which statements are correct regarding the kinetic properties of gases, we will analyze each statement one by one.

### Step 1: Analyze the first statement
**Statement**: The RMS translational speed for different ideal gas samples at the same temperature is not necessarily the same; it depends upon molar mass.

**Analysis**: The formula for the root mean square (RMS) speed (\(V_{rms}\)) of a gas is given by:
\[ V_{rms} = \sqrt{\frac{3RT}{M}} \]
where \(R\) is the universal gas constant, \(T\) is the temperature in Kelvin, and \(M\) is the molar mass of the gas. Since the molar mass \(M\) varies for different gases, the RMS speed will also vary even if the temperature is the same. Thus, this statement is **correct**.

### Step 2: Analyze the second statement
**Statement**: The speed of a particular gas molecule can be greater than the RMS speed of the sample.

**Analysis**: The RMS speed is a statistical measure of the speeds of gas molecules in a sample. It is possible for individual molecules to have speeds that are higher than the RMS speed. For example, if we have molecules with speeds of 1 m/s, 2 m/s, and 3 m/s, the RMS speed will be less than the highest speed (3 m/s). Therefore, this statement is also **correct**.

### Step 3: Analyze the third statement
**Statement**: The temperature of an ideal gas doubles from 100°C to 200°C. The average kinetic energy of each particle gets also doubled.

**Analysis**: The average kinetic energy of gas particles is given by:
\[ KE = \frac{3}{2} k_B T \]
where \(k_B\) is the Boltzmann constant and \(T\) is the temperature in Kelvin. To correctly analyze the change in kinetic energy, we must convert the temperatures to Kelvin:
- 100°C = 373 K
- 200°C = 473 K

The doubling of temperature in Celsius does not correspond to doubling in Kelvin. Therefore, the average kinetic energy does not double when the temperature is increased from 100°C to 200°C. This statement is **incorrect**.

### Step 4: Analyze the fourth statement
**Statement**: It is possible for both the pressure and the volume of a monoatomic ideal gas to change simultaneously without causing the internal energy of the gas to change.

**Analysis**: The internal energy (\(U\)) of an ideal gas is related to its temperature:
\[ \Delta U = nC_v \Delta T \]
If the process is isothermal (constant temperature), then \(\Delta T = 0\) and thus \(\Delta U = 0\). In an isothermal process, pressure and volume can change simultaneously while keeping the internal energy constant. Therefore, this statement is **correct**.

### Conclusion
Based on the analysis:
- **Correct Statements**: 1, 2, and 4
- **Incorrect Statement**: 3

### Final Answer
The correct statements are: **1st, 2nd, and 4th**. The 3rd statement is incorrect.

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