Helium stars are really interesting thermodynamic systems because they can be modeled as isolated spheres of N ideal gas particles held together by gravity. Considering this, prove that for such a system, the gravitational potential energy is -2 times its total kinetic energy (you may prove it by considering 2 identical particles orbiting around their center of mass, see picture.) express the total energy of the star in terms of its average temperature. determine an expression for the star’s heat capacity. calculate the entropy in terms of average temperature. calculate the entropy as a function of total energy, U, then plot S vs. U. Explain your observations: i.e. what is happening with temperature? What other systems exhibit this behavior?

Helium stars are really interesting thermodynamic systems because they can be modeled as isolated spheres of N ideal gas particles held together by gravity. Considering this, prove that for such a system, the gravitational potential energy is -2 times its total kinetic energy (you may prove it by considering 2 identical particles orbiting around their center of mass, see picture.) express the total energy of the star in terms of its average temperature. determine an expression for the star’s heat capacity. calculate the entropy in terms of average temperature. calculate the entropy as a function of total energy, U, then plot S vs. U. Explain your observations: i.e. what is happening with temperature? What other systems exhibit this behavior?

Similar questions

So each four dot shows four different states for an ideal gas. P is the pressure and the other one is the density of the gas. Is temperature of state 1 less or greater than the state 2? Can you please explain why?
An ideal gas, initially at a pressure of 10.3 atm and a temperature of 312 K, is allowed to expand adiabatically until its volume doubles. What is the gas’s final temperature, in kelvin, if the gas is monatomic? What is the gas’s final pressure, in atmospheres, if the gas is diatomic?
(b) Consider the following heat system on the real line: U - U = 0, XER, 1>0 %3D u(x, 0) = | sin x), rER. i. Use the fundamental solution of the heat equation to write down a solution u to the system above as an integral. ii. Show that the solution u that you have found is bounded by 1.
Problem 4: Consider a cylinder with a movable piston containing n moles of an ideal gas. The entire apparatus is immersed in a constant temperature bath of temperature T Kelvin. The piston pushes slowly outward on an external body which matches the force momentarily at each instant so that the gas expands quasi-statically from a volume V1 to V2 at constant temperature T. The isothermal process is shown in the figure above, where the pressure p is related to the volume V by the ideal gas law as follows: pV = nRT, where R is the gas constant. Part (b) For n = 3 moles, T = 350 K, and V2 = 2.5V1, determine the work done by the gas on the external body. The gas constant is R = 8.314 J K-1 mol-1.
This is a calculation only. Energy2d isn’t able to do phase changes as far as I’ve learned. There was a different simulation for this but it is not currently free. You combine 50g of ice at -10oC with 150g of liquid water at 75oC. After a few minutes, you measure the final equilibrium temperature of all of the H2O to be 35.1 oC. Use this information to “experimentally” determine the heat of transformation of water, Lfusion. cwater=4190 J/kgK, cice=2090 J/kgK Show all of your work and compare to the accepted value Lfusion=3.33x105 J/kg.