Thermodynamics - thermal energy?

[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?

 

[Chestermiller]

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 E_total=1.5nRT. But, from the ideal gas law, nRT = PV. So, what is E_total?

 

[Khashishi]

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.

 

[Andrew Mason]

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

 

[sardar]

Thermodynamics is the study of energy and its transformations, including thermal energy. Thermal energy refers to the internal energy of a system due to the random motion of its particles. This energy is related to the translational kinetic energy of the particles, which is given by the equation E(kin)=1.5kT, where k is the Boltzmann constant and T is the temperature of the system.

To find the total thermal energy of a system, we need to consider the volume and pressure of the system as well. This is because the thermal energy of a system is directly proportional to its temperature, but also depends on its volume and pressure. Therefore, the total thermal energy can be calculated using the ideal gas law, which states that the product of pressure and volume is proportional to the temperature of a gas at a constant number of moles. The equation for the ideal gas law is PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the gas constant, and T is the temperature.

By rearranging this equation, we can find the thermal energy of a system as E= (nRT)/2. This equation takes into account the translational kinetic energy of the particles, as well as the volume and pressure of the system. Therefore, to find the total thermal energy of a system of a given volume and pressure, we would need to know the number of moles of the gas and its temperature. From there, we can use the ideal gas law to calculate the thermal energy.

It is important to note that this equation is valid for ideal gases, which follow the ideal gas law perfectly. In real systems, there may be other factors at play, such as intermolecular forces, which can affect the thermal energy of the system. In such cases, more complex equations or experimental data may be needed to accurately determine the thermal energy of the system.