c) Derive the Schwarzschild criterion for the onset of convection in an ideal gas, namelyd ln Td ln P7-1YExplain all steps in your derivation, and justify any assumptions that you make.d) In a region of convective instability near the surface of a solar-type star of total mass M, the temperature and pressure arerelated approximately by the expression P KT5/2. Show that the temperature gradient for an ideal gas in hydrostatic=equilibrium in this convection zone is given bydTdr2Gm(r)μ5Rr²Further, assuming that the mass in the convection zone is small compared to M, show that at a depth h measured from the top ofthe convection zone, the temperature is approximately given byT = Ts +2GMμ-h₂5RR²when his small compared to R, and Ts is the temperature at the top of the convection zone.

To derive the Schwarzschild criterion for the onset of convection in an ideal gas, we start with the…

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c) Derive the Schwarzschild criterion for the onset of convection in an ideal gas, namely dln T d ln P 7-1 Y Explain all steps in your derivation, and justify any assumptions that you make.