Explanation

The root mean square (rms) velocity of a particle is a measure of the average speed of the particles in a gas. It is calculated as the square root of the average of the squares of the individual velocities of the particles. The rms velocity is directly proportional to the square root of the temperature and inversely proportional to the square root of the molar mass of the gas.

Effect of Pressure on Rms Velocity

When the pressure is increased by two times while keeping the temperature constant, the rms velocity of the particles also changes. Let's analyze the effect of pressure on the rms velocity.

1. Increase in Pressure
- When the pressure is increased, the particles in the gas become more closely packed together.
- The increased pressure leads to a higher frequency of collisions between particles.
- As a result, the average kinetic energy of the particles increases.

2. Temperature Constant
- It is mentioned that the temperature is constant in this scenario.
- Temperature is a measure of the average kinetic energy of the particles in a gas.
- Since the temperature is constant, the average kinetic energy remains the same.

3. Relation between Kinetic Energy and Rms Velocity
- The rms velocity is related to the average kinetic energy of the particles.
- The average kinetic energy is directly proportional to the square of the rms velocity.

4. Effect on Rms Velocity
- As the pressure increases, the average kinetic energy of the particles increases.
- Since the temperature is constant, the increase in average kinetic energy has to be compensated by an increase in the rms velocity.
- Therefore, the rms velocity of the particles increases when the pressure is increased by two times while keeping the temperature constant.

Conclusion

In conclusion, when the pressure is increased by two times while keeping the temperature constant, the rms velocity of the particles also increases. This is because the increased pressure leads to a higher frequency of collisions between particles, causing an increase in the average kinetic energy. Since the temperature is constant, the increase in average kinetic energy is reflected in an increase in the rms velocity.

Rms velocity is v bcoz its only depends on temperature.