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!

 

[Nate810]

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.

 

[ogb p]

I would like to first clarify that the Crooke's radiometer is a device used to demonstrate the effects of radiation pressure and not directly related to the kinetic theory of gases. However, the principles of the kinetic theory of gases can be applied to understand the behavior of gases within the radiometer.

To calculate the net force on one blade of the radiometer, we can use the formula for pressure (P= nRT) where n is the gas density, R is the gas constant, and T is the temperature. In this case, we have the temperature difference between the black and white surfaces as 30C, which is equivalent to 303K. Plugging in the given values, we get P= 2.5 x 10^20 x 8.314 x 303 = 6.1 x 10^24 Pa.

To calculate the net force, we can use the formula F=PA, where A is the area of one blade (1cm^2 or 0.0001m^2). Thus, the net force on one blade would be 6.1 x 10^24 x 0.0001 = 6.1 x 10^20 N.

In the limit of vanishing gas density, we can assume that the gas molecules are widely spread out and have very low kinetic energy, resulting in a decrease in pressure and net force on the blades. In this case, the net force would approach zero as the gas density approaches zero.

Regarding your suggestion of using the formula for kinetic energy, it is not directly applicable in this scenario as it calculates the average kinetic energy of gas molecules, not the net force on the blades.

I hope this explanation helps in solving the problem and understanding the concept of the kinetic theory of gases in relation to the Crooke's radiometer.