The surface of the Sun has a temperature of 5500 C and the temperature of deep s

Question

The surface of the Sun has a temperature of 5500 C and the temperature of deep space is 3.0 K. Find the entropy increase produced by the Sun in one day, given that it radiates heat at the rate of 3.80x10^26 W. How much work could have been done if this heat had been used to run an ideal heat engine?

Explanation / Answer

sun temp (T1 = 5500+273 K) >> source >> losses heat in 1 day = Q1 Q1 = 3.80x10^26 (W)*(24*3600 sec) Joule Q1 = 3283.2*10^28 J --------------------------------------… Deep space >> sink temp (T2 = 3 K) >> gains heat in 1 day = Q1 -------------------------------- change in entropy dS = dQ/T >> defined as heat gained/lost per unit of temp (deg K) at constant temp. ds = + ve when heat gained (disorder increases) ds = - ve when heat lost (disorder decreases) net change in entropy = dS = - Q1/T1 + Q1/T2 dS = Q1 [T1 - T2] / T1 T2] = Q1[5770/5773*3] dS = 3283.2*10^28 *0.333 dS = + 1093.34*10^28 J/deg K dS = 10.93*10^30 J/K b) work done for ideal pump efficiency of pump = (T1-T2)/T1 = Work done/Q1 W = Q1 *[5770/5773] W = 3281.5*10^28 Joule W = 32.81*10^30 J

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