Question

A hydroelectric power plant produces 1200MW of power at 85% efficiency. A nuclear power plant produces 1200MW of power at 40% efficiency. How much is more power wasted in the nuclear power plant than the hydroelectric power plant?

I did `1200*(0.85-0.4)=540MW`, but the answer is 1600MW. Some explanation plz! Thanks!

Answer 1

See the explanation below

Explanation:

The output power of the hydroelectric plant is `P_(ho)=1200MW`

The efficiency is `eta_h=85%=0.85`

Let, the input of the hydroelectric plant is `=P_(hi)`

The efficiency is `eta_n=P_(ho)/P_(hi)`

Therefore,

`P_(hi)=P_(ho)/eta_(h)=1200/0.85MW`

The power wasted by the hydroelectric plant is

`P_(hw)=(1200/0.85-1200)MW`

The output power of the nuclear plant is `P_(no)=1200MW`

The efficiency is `eta_n=40%=0.40`

Let, the input of the nuclear plant is `=P_(ni)`

The efficiency is `eta_h=P_(no)/P_(ni)`

Therefore,

`P_(ni)=P_(no)/eta_(n)=1200/0.40MW`

The power wasted by the nuclearplant is

`P_(nw)=(1200/0.40-1200)MW`

The difference between the waste of the nuclear plant and the hydroelectric plant is

`DeltaP_w=P_(nw)-P_(hw)=(1200/0.40-1200)-(1200/0.85-1200)`

`=1200/0.40-1200-1200/0.85+1200`

`=1200/0.4-1200/0.85`

`=3000-1412`

`=1588MW`

`~=1600MW`

I hope that this will help!!