Consider a 1 MW power plant (this is the useful output in the form of electric e

Question

Consider a 1 MW power plant (this is the useful output in the form of electric energy) that operates between 30C and 450C at 65% of the Carnot efficiency. This is enough electric energy for about 750 homes. One way to use energy more efficiently would be to use the 30C "waste" energy to heat the homes rather than releasing that heat energy into the environment. This is called cogeneration, and it is used in some parts of Europe but rarely in the United States. The average home uses 70 GJ of energy per year for heating. For estimating purposes, assume that all the power plant's exhaust energy can be transported to homes without loss and that home heating takes place at a steady rate for half a year each year.

How many homes could be heated by the power plant?

my answer come out to be

243 homes which is wrong. Can any body help me with this please?

243 homes which is wrong. Can any body help me with this please?

Explanation / Answer

given

the out put power, P = 1 MW

so,

Workdone per one second, W = 1*10^6 J

Efficiency of the power plant, e = 1 - Tc/Th

= 1 - (30 + 273)/(450 + 273)

= 0.5809

we know, e = W/Qin

Qin = W/Qin

= 1*10^6/0.5809

= 1.72*10^6 J

now use, Qout = Qin - W

= 1.72*10^6 - 1*10^6

= 0.72*10^6 J (per every second)

Exhaust energy from power plant in half year = (365/2)*24*60*60*0.72*10^6

= 1.135*10^13 J

Energy used by each home in every year = 70 GJ = 70*10^9 J

so, no of home, N = 1.135*10^13/(70*10^9)

= 162 homes <<<<<<<<---------------------------Answer

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