Kittel, Ch4-5. Surface temperature of the Earth. Calculate the temperature of the surface of the Earth on the assumption that as a black body in thermal equilibrium it reradiates as much thermal radiation as it receives from the Sun. Assume also that the surface of the Earth is at a constant temperature over the day-night cycle. Use T₂=5800K; R₂ = 7x10⁰ cm; and the Earth-Sun distance of 1.5x10¹³ cm.

c) Derive the Schwarzschild criterion for the onset of convection in an ideal gas, namely d ln T d ln P 7-1 Y Explain 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 are related 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 by dT dr 2Gm(r)μ 5Rr² Further, assuming that the mass in the convection zone is small compared to M, show that at a depth h measured from the top of the convection zone, the temperature is approximately given by T = Ts + 2GMμ -h₂ 5RR² when his small compared to R, and Ts is the temperature at the top of the convection zone.