HELP!!! I Need a Physics Genius!!! RMS Speed?

Question

1.) If two different gases are at the same temperature, the root mean square speed of their molecules must be the same for both of them.

True or Flase?

2.) If the root mean square speed of gas molecules is doubled, then both its pressure and its absolute temperature will also be doubled.

True or False?

3.) Doubling the root mean square speed of the molecules of a gas has a greater effect on its pressure than doubling the number of gas molecules in the container.

True of False?

4.) If two different gases are at the same temperature, the average translational kinetic energy per molecule must be the same for both of them.

True or False?

5.) Water turns to ice when it is placed in a freezer. During this process, the entropy of this water has decreased.

True or False?

Thank you for your time and consideration!!!!

Answer 1

Root mean square speed of the particles of an ideal gas is derived by integration of the square of the Maxwell-Boltzmann distribution function, and its value is sqrt(3*R*T/M).

Remember that R is constant; T is temperature; and M is the molecular mass which varies from gas to gas.

Therefore,

1) is false, because the values of M will probably differ.

2) The absolute temperature T will be multiplied by 4 if the root mean square speed is doubled, since T is within the square root sign (square both sides and you'll see what I mean). By the ideal gas law, the pressure also quadruples. Therefore, this statement is false.

3) Doubling the RMS speed will quadruple the temperature, which again quadruples the pressure. On the other hand, doubling the number of particles only doubles the pressure (ideal gas law). Therefore 3) is true

4) The average translational kinetic energy is given by 3/2 kT for any ideal gas, where k is the Boltzmann constant. Since T is the same for both gases, 4) is true.

5) True, because it goes from a more disorderly liquid to a more orderly solid. (Note that the entropy of the universe increases however.)