Determining temperature of heat bath

[fizziks]

I have a bunch of degenerate particles in a heat bath, which I can "measure" some of their properties to approximate the temperature of the heat bath. Like energy at ground state, 2nd, etc, and their degeneracies.

But I was told that the exact temperature of the heat bath cannot be measured and only the approximation can be made.

I was reading my stats mechanics book and all I can find is something about thermal equilibrium requiring a Boltzmann distribution and a formulation to find Temperature of a heat bath of non-degenerate particles.

I tried searching the internet for some more information but I keep ending up with research papers that have nothing to do with my question.

 

[tim_lou]

do some counting and calculate the multiplicity of the system in terms of some known qualities. then find the entropy and the temperature is equaled to:
$$T=\left ( {\frac{\partial S}{\partial U}}\right )^{-1}_{V,N}$$

 

[astrokreng]

it is important to understand the limitations of our measurements and the underlying principles that govern the systems we are studying. In the case of determining the temperature of a heat bath, there are several factors to consider.

Firstly, the concept of temperature is a macroscopic quantity that describes the average kinetic energy of a system. In the case of a heat bath, which consists of a large number of particles in thermal equilibrium, the temperature can be approximated by measuring the average energy of the particles.

However, as you have mentioned, the exact temperature of a heat bath cannot be measured. This is because temperature is a statistical concept and the precise energy of each particle in the heat bath cannot be determined. Additionally, the concept of thermal equilibrium, which is necessary for the Boltzmann distribution to hold, requires that the system is isolated and not interacting with its surroundings. This is often not the case in real-world scenarios.

Furthermore, the Boltzmann distribution and formulation for determining the temperature of a heat bath are based on the assumption that the particles in the system are non-degenerate, meaning that they can occupy any energy state. In reality, many systems have degenerate particles, which can significantly affect the temperature measurement.

In summary, while it is possible to approximate the temperature of a heat bath by measuring certain properties of its particles, it is important to recognize the limitations of these measurements and the assumptions that are being made. it is important to continuously seek a deeper understanding of the underlying principles and to critically evaluate the accuracy of our measurements.