# Thermodynamics - thermal energy?

• iScience

#### iScience

The thermal energy comes from the translational kinetic energy right? The relationship between the two being E(kin)=1.5kT

how would i go about finding the total thermal energy of a system of a given volume and pressure?

Your equation is for the average kinetic energy per molecule. Multiply by avagadro's number to get the kinetic energy (internal energy) per mole, or, equivalently, replace the k in your equation by the gas constant R. If you have n moles, then Etotal=1.5nRT. But, from the ideal gas law, nRT = PV. So, what is Etotal?

You have a long way to go in your understanding. Thermal energy includes all kinds of energy, including translational, rotational, vibrational kinetic energies and other forms of energy.
Check out Equipartition theorem - Wikipedia, the free encyclopedia
Your second sentence is mostly ok for the case of a monoatomic ideal gas. That's the kinetic energy of each atom.

In regards to your question, it depends on what your system is. If it is an ideal gas, then you can use the ideal gas law ##PV = nkT##. The thermal energy is ##dnkT##, where d is the number of degrees of freedom, 3 for a monoatomic gas.

The thermal energy comes from the translational kinetic energy right? The relationship between the two being E(kin)=1.5kT

how would i go about finding the total thermal energy of a system of a given volume and pressure?
I would recommend against using the term "thermal energy". It is used inconsistently and may refer to either heat or internal energy so it can be confusing. You should use "heat" or "heat flow" to refer to the transfer of energy between two states by means other than mechanical work. Or you may use "internal energy" to describe the energy content of a system in a particular state.

Temperature is a measure of the average translational kinetic energy of a collection of molecules in thermal equilibrium. For a monatomic ideal gas, the internal energy of the gas, U = nCvT = 3nRT/2. For more complicated molecules, which have active vibrational and/or rotational modes, and intermolecular forces, the internal energy consists of translational, rotational, vibrational as well as potential energy.

AM