Kinetic Theory Of Gases - radiometer

[InnealtóirLeTeacht]

This is a question relating to a Crooke's radiometer:

Assume that due to absorption, the local temperature close to the black surface is T = 50C, while the temperature close to the white surface is T = 20C. For a gas with density n = 2:5 x 10E20m-3, compute the net force on one blade of area 1cm2. What do you expect in the limit of vanishing gas density?

I would appreciate any help you can give, if anyone knows what the 'limit of vanishing gas density' is or has any equations that would be useful in solving the problem.

I'm sure this is incorrect but can you use the formula for Kinetic Energy- KE=3/2 kT and subtract the kinetic energy by the white surface from that of the black surface?

Thanks!

 

[member 553083]

No, this is not the correct approach. The net force on one blade of the Crooke's radiometer can be calculated using the following equation: F = nk(T_b - T_w)A, where n is the number density of the gas, k is Boltzmann's constant, T_b is the temperature of the black surface, T_w is the temperature of the white surface, and A is the area of the blade. Substituting the given values yields a force of 2.5 x 10^-16 N. In the limit of vanishing gas density, the force would approach zero. This is because in the absence of molecules to absorb the thermal radiation, there is no temperature difference between the black and white surfaces, thus no net force would be generated.