Question

A California geothermal power plant generates 4.3 MW by extracting 24 MW of heat from an underground source at 108°C and then discharging waste heat into the 17°C air.

What is the actual efficiency of the plant?

What is the theoretical efficiency?

Answer 1

given,

Power generated,P_0 = 4.3 MW

Power extracted = 24 MW

Temperature of source,T₁ = 108°C

Temperature of discharge,T₂ = 17°C

a) Actual efficiency

`\eta =(P_0)/(Power\ extracted)* 100`

`\eta = (4.3)/(24)* 100`

`\eta = 17.92\ \%`

b) Maximum theoretical efficiency

`\eta_(max)=(1-(T_2)/(T_1))* 100`

`\eta_(max)=(1-(273+17)/(273+108))* 100`

`\eta_(max) = 23.88\ \%`