a) A qantity of heat Q= 200J is released from a heat engine into the environment

Question

a) A qantity of heat Q= 200J is released from a heat engine into the environment, which is at a temperature Te. Make a chart listing how much entropy (delta S) this corresponds to for the values of environmental temperatures,

Te= 100, 300, 500, 10^3, 10^4 K

b) Suppose you are designing an engine. Using the second law of thermodynamics you compute that an amount of entropy (delta S(out)= 1J / K) will need to leave the machine. For the same list of temperatures Te, how much waste heat Q(out) , is released into the environment? So, what are the best conditions to minimize waste heat?

Explanation / Answer

a) change in entropy = heat/Te

at T = 100 , change in entropy = 200/100   =   2 j/k

at T = 300 , change in entropy = 200/300   =   0.66 j/k

at T = 500 , change in entropy = 200/500   =   0.4 j/k

at T = 1000 , change in entropy = 200/1000 =   0.2 j/k

at T = 10^4 , change in entropy = 200/10^4 =   0.02 j/k

b)    eat =change in entropy*Te

at T = 100 , heat =1*100 = 100 j

at T = 300 , heat =1*300 = 300 j

at T = 500 , heat =1*500 = 500 j

at T = 1000 , heat =1*1000 = 1000 j

at T = 10^4 , heat =1*10^4 = 10^4 j

to minimize wasted heat , reduce temperatur

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