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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 :

Answer

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

   [tex]\eta =\dfrac{P_0}{Power\ extracted}\times 100[/tex]

   [tex]\eta = \dfrac{4.3}{24}\times 100 [/tex]

   [tex]\eta = 17.92\ \%[/tex]

b) Maximum theoretical efficiency

   [tex]\eta_{max}=(1-\dfrac{T_2}{T_1})\times 100[/tex]

   [tex]\eta_{max}=(1-\dfrac{273+17}{273+108})\times 100[/tex]

   [tex]\eta_{max} = 23.88\ \%[/tex]

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