Two containers of identical size contain 1 mole each of the same ideal monatomic gas. Container 1 is at a higher temperature than container 2. Are the following statements true sometimes, always or never (justify your answer)  If the fastest 10 % of gas atoms in container 1 escape, the most probable speed of the remaining gas atoms will remain the same

The statement, "If the fastest 10% of gas atoms in container 1 escape, the most probable speed of the remaining gas atoms will remain the same," is **always true**.

### Justification:

For an ideal gas, the distribution of speeds follows the Maxwell-Boltzmann distribution. This distribution is characterized by three main speeds: 
1. **Most probable speed ( \(v_{\text{mp}}\) ):** The speed at which the greatest number of particles are moving.
2. **Average speed ( \(v_{\text{avg}}\) ):** The average speed of all particles.
3. **Root mean square speed ( \(v_{\text{rms}}\) ):** The square root of the average of the squares of the speeds.

The most probable speed, \(v_{\text{mp}}\), is determined by the temperature \(T\) of the gas and is given by:
\[
v_{\text{mp}} = \sqrt{\frac{2 k_B T}{m}}
\]
where \( k_B \) is the Boltzmann constant, and \( m \) is the mass of a single atom of the gas.

When the fastest 10% of atoms escape, they take away energy, effectively decreasing the total internal energy of the remaining gas. However, in the context of the Maxwell-Boltzmann distribution, **the most probable speed is a function of the temperature alone**, which has not changed by simply removing atoms. Therefore, the distribution of the remaining particles will still have the same most probable speed as before the escape of the fastest atoms, although the overall average and root mean square speeds would decrease.

This characteristic makes the statement **always true**.

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Would you like further details on the Maxwell-Boltzmann distribution, or have any other questions?

### Related Questions:
1. How does removing the fastest 10% of atoms affect the average kinetic energy of the remaining atoms?
2. What is the relationship between temperature and the root mean square speed in an ideal gas?
3. Why does the Maxwell-Boltzmann distribution characterize the most probable speed independently of particle count?
4. How would this scenario differ if the gas were not ideal?
5. What are other ways to change the most probable speed in a gas?

### Tip:
The most probable speed in a gas is only affected by changes in temperature, not by the removal of faster or slower molecules.

Two containers of identical size contain 1 mole each of the same ideal monatomic gas. Container 1 is at a higher temperature than container 2. Are the following statements true sometimes, always or never (justify your answer) If the fastest 10% of gas atoms in container 1 escape, the most probable speed of the remaining gas atoms will remain the same.

Explore whether the most probable speed in an ideal gas remains constant when the fastest 10% of gas atoms escape. Understand the impact on Maxwell-Boltzmann distribution and key thermodynamic principles with detailed explanations and formulas. Ideal for college-level physics students.

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