Does Doubling Gas Molecules Affect RMS Speed?

In summary, the question asks if the rms speed of an ideal gas in a container of constant volume and pressure will change when the number of molecules is doubled. The answer is no, it will stay the same. The formula to calculate the final rms speed is v_{rms} = \sqrt { \frac {3 R T} {m} }, where T is the temperature and m is the mass of one mole of the gas molecule.
  • #1
ajmCane22
33
0

Homework Statement



An ideal gas is kept in a container of constant volume. The pressure of the gas is also kept constant
(a) If the number of molecules in the gas is doubled, does the rms speed increase, decrease, or stay the same?
(b) If the initial rms speed is 1300 , what is the final rms speed?

Homework Equations



PV=nRT...I think

The Attempt at a Solution


For part I, I believe the rms speed decreases. So if the only thing changing is the number of molecules wouldn't doubling the molecules cause rms to decrease by half? I know the answer is no, because the computer said so, I'm just not sure why it's wrong. And how much does it decrease then?
 
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  • #2
If the volume and the pressure must remain constant, the only way to get in more molecules is cooling the gas, and let in more gas to keep the pressure constant.

If the original tempererature was T, what is the new temperature?

After you've found it use

[tex] v_{rms} = \sqrt { \frac {3 R T} {m} } [/tex]

where m is the mass of one mole of the gas molecule
 

Related to Does Doubling Gas Molecules Affect RMS Speed?

What is kinetic theory?

Kinetic theory is a scientific explanation of how particles in a gas behave. It states that all particles are in constant motion and that the temperature of a gas is directly related to the average kinetic energy of its particles.

How does kinetic theory explain gas pressure?

Kinetic theory explains that the pressure exerted by a gas is caused by the constant collisions of its particles with the walls of its container. The more collisions, the higher the pressure.

What factors affect gas pressure according to kinetic theory?

According to kinetic theory, gas pressure is affected by the number of particles, the temperature, and the volume of the container. Increasing any of these factors will result in an increase in gas pressure.

How is temperature related to the kinetic energy of gas particles?

The kinetic theory states that the temperature of a gas is directly proportional to the average kinetic energy of its particles. As the temperature increases, the particles move faster and have higher kinetic energy, resulting in higher pressure.

What is the difference between ideal and real gases according to kinetic theory?

Ideal gases are theoretical and do not account for intermolecular forces between particles, while real gases do. This means that real gases may deviate from the predictions of kinetic theory at high pressures or low temperatures.

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