Keeping the number of moles, volume and pressure the same, which of the following are the same for all ideal gas?

Options

A. rms speed of a molicule
B. density
C. temperature
D. average of magnitude of momentum.

Explanation

To solve the question, we need to analyze the properties of ideal gases under the condition where the number of moles (n), volume (V), and pressure (P) are held constant. We will use the ideal gas law and the definitions of various properties of gases to determine which quantities are the same for all ideal gases.

### Step-by-Step Solution:

1. **Understand the Ideal Gas Law**:
The ideal gas law is given by the equation:
\[ PV = nRT \]
where:
- \( P \) = pressure
- \( V \) = volume
- \( n \) = number of moles
- \( R \) = universal gas constant
- \( T \) = temperature

2. **Identify Given Conditions**:
According to the question, the number of moles \( n \), volume \( V \), and pressure \( P \) are constant. This implies that the product \( PV \) is also constant.

3. **Determine the Temperature**:
Since \( P \), \( V \), and \( n \) are constant, we can rearrange the ideal gas law to find the temperature:
\[ T = \frac{PV}{nR} \]
Since \( P \), \( V \), \( n \), and \( R \) are constant, it follows that \( T \) must also be constant for all ideal gases under these conditions.

4. **Examine Other Properties**:
We need to check if other properties such as RMS speed, density, and average momentum are the same for all ideal gases.

- **RMS Speed**: The root mean square speed (\( V_{RMS} \)) is given by:
\[ V_{RMS} = \sqrt{\frac{3RT}{M}} \]
where \( M \) is the molar mass of the gas. Since \( M \) varies for different gases, \( V_{RMS} \) will also vary, which means it is not the same for all ideal gases.

- **Density**: Density (\( \rho \)) is defined as:
\[ \rho = \frac{m}{V} = \frac{nM}{V} \]
Since \( M \) (molar mass) varies for different gases, the density will also vary and is not the same for all ideal gases.

- **Average Momentum**: The average momentum (\( P_{avg} \)) can be expressed as:
\[ P_{avg} = m \cdot V_{avg} \]
where \( m \) is the mass and \( V_{avg} \) is the average speed. Since the mass (related to molar mass) varies for different gases, the average momentum will also vary.

5. **Conclusion**:
The only quantity that remains the same for all ideal gases under the given conditions (constant \( n \), \( V \), and \( P \)) is the temperature \( T \). Therefore, the answer to the question is that the temperature is the same for all ideal gases.

### Final Answer:
**Temperature is the same for all ideal gases when the number of moles, volume, and pressure are kept constant.**