Converting sunlight to electricity with solar cells has an efficiency of 15%. It
ID: 249968 • Letter: C
Question
Converting sunlight to electricity with solar cells has an efficiency of 15%. It's possible to achieve a higher efficiency (though currently at higher cost) by using concentrated sunlight as the hot reservoir of a heat engine. Each dish in (Figure 1) concentrates sunlight on one side of a heat engine, producing a hot-reservoir temperature of 540 C . The cold reservoir, ambient air, is approximately 26 C. The actual working efficiency of this device is 30%.
What is the theoretical maximum efficiency?
Express your answer using two significant figures.
emax = %Explanation / Answer
The theoretical maximum efficiency of any heat engine is the Carnot efficiency, which is one minus the ratio of the cold temperature to the hot temperature. (These have to be *thermodynamic* temperatures, meaning they're measured on a scale that puts "zero" at absolute zero. Kelvin is a thermodynamic temperature scale, while Fahrenheit and Celsius are not.)
To convert from degrees Celsius to Kelvin, add 273.15. (It's just "Kelvin," not "degrees Kelvin.")
The cold temperature:
TC = 26 degC = 299.15K
The hot temperature:
TH =540 degC = 813.15 K
The Carnot efficiency:
eff = 1 - (TC / TH) = 1 - (299.15 K / 813.15 K)
=0.6321
So the theoretical maximum efficiency is 63.21 %.