A large electrical power station generates 1000 MW of electricity with an effo -

Question

A large electrical power station generates 1000 MW of electricity with an effo -Y of 25 % a) How much heat does the power station need to generate this amount of electricity in one day? Oh- b) How much heat is exhausted to the environment in one day? c) The exhaust heat is transferred to the ambient air at 15 °C. What is the change in entropy of the surrounding air in one day? J/K d) The heat driving the generators is in the form of superheated steam at 330 °C. If a Carnot engine had been used instead what would it's efficiency be? Efficiency # e) How much work was lost (left undone) because a Carnot engine was not used?

Explanation / Answer

a) In 1s, 1000MJ is produced, so in 1 day, 1000*24*3600= 8.64*10^7 MJ is produced. Efficiency being 25%, heat required to produce this much electricity is Qh= 8.64/0.25 *10^7MJ = 34.56*10^7MJ= 3.456*10^14 J

b) Remaining heat, which is 0.75*Qh, is exhausted to environment. So, Qc= 2.592*10^14 J

c) change in entropy is Qc/(273+15)K = 9*10^11 J/K

d) carnot cycle , with temperature range as 330+273= 603K and 15+273= 288K, efficiency is 1 - 288/603= 52.24%

e) carnot engine is having 52.24-25= 29.24% more efficiency here. So, in one day, work lost or left undone is 0.2924*Qh= 1.01*10^14 J

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