Solving for degeneracy electron cloud temperature

[kamui1]

Homework Statement

Assume degeneracy starts to dominate approximately when the pressure expected from a completely degenerate electron gas equals that expected from an ideal gas (P_rel_e=P_ideal=1/2Ptotal) Show that the temperature at that point, which we assume will be the maximum reached, is given by T_max is true

Relevant Equations

Tmax= 7.7x10^7 K mu*mu_e^5/3*(M/M_solar)^5/3
P_rel_e = K(ro/mu_e*m_h)^5/3
P_ideal = nKT

When I try P_rel_e = P_ideal I couldn't get a single number that is close to the given T_Max. It might be that I used the wrong equations but I am not sure. Can anyone give me some guidence on this question?

 

[Nate810]

To solve this question, you will need to use the ideal gas law equation and the equation of state for a real gas. The ideal gas law equation is P*V = n*R*T, where P is the pressure, V is the volume, n is the number of moles, R is the universal gas constant, and T is the temperature. The equation of state for a real gas is PV = nRT + a(n2/V2), where a is an empirical constant that depends on the type of gas.To find the maximum temperature with a given pressure, you will need to solve the equation of state for the temperature. First, rearrange the equation of state to solve for T:T = (PV - a(n2/V2))/(nR)Then, substitute the known values of P, V, n, and R into the equation to solve for T. You can then compare the calculated maximum temperature to the given value to see if it is close.