Thermodynamics and Kinetics of a Brownian Motor

Abstract: There are two different temperatures in physics, so we can’t know the change of the temperature in the relativity theory. We will discuss those two temperatures in this paper. (We only discuss the temperature of the objects in no gravitational field now)
Keywords: temperature; relativity theory; radiation
Two different temperatures
1, Temperature in the thermal conduction
Temperature in the thermal conduction shows the intensity of the random thermal motion of the particles in the object. We can use the kinetic energy of the particles to show the intensity of the random thermal motion.
E=3/2kT
We can measure this temperature by using the spirit thermometer. This temperature shows the really kinetic energy of the particles, we can use this temperature to judge the state of the objects, like does the water should become the ice in this condition. If there is an object A which is moving with velocity v, and there are many spirit thermometers (A1, A2, A3...) which are static in all points of this inertial frame, and we assume the measure doesn’t use time. We can get the temperature T0, if we put another spirit thermometer B on the object, we can get the temperature T1 by B , we think that T0=T1 because the intensity of the random thermal motion of the particles in the object only depend on the relative motion between the particles, and the relative motion between the particles is same in two different inertial frames. So if in an inertial frame a bottle of water is liquid, in any other inertial frame, it must be liquid, it can’t be ice.

2, Temperature in the thermal radiation (black body)
We can know the temperature of an object by measuring the thermal radiation.
N=1/[e^(hv/kT)-1]
T=hv/kln(1/N+1)
But the Doppler Effect and the effect of the relativity theory will change the frequency of the radiation. If we use the radiation to measure the temperature of the object A, and the temperature is T2, we will find T2≠T0 because the speed of the object A. We will find T2=T0 when the object A is static in our inertial frame.
3, Temperature and inertial frame
If there is an inertial frame, in this inertial frame, we have a cesium-beam atomic clock. If we make the temperature of the inertial frame is T3, we will know that the kinetic energy of the particles in this inertial frame E3=3/2kT3, we assume the kinetic energy of the cesium atom is E3. E3=(m0c^2/γ)-m0c^2, γ=√1-(v/c)^2, m0 is the rest mass of the cesium atom, we can get the speed of the cesium atomic. If we use this cesium atom to measure time, and use a common ruler to measure the distance, we will get a different speed of light: c1=c/γ. We can know that the reference system which has a temperature is a non inertial frame. And we can know that the relativity theory ( special relativity and general relativity) only describe the objects which reached absolutely zero and have no zero-point energy. Relativity theory is a theory in absolutely zero and non quantum mechanics.