Question

Calculate the maximum possible efficiency of a power plant that burns natural gas at a temperature of 600k, with low temperature surroundings at 300k. How much more efficient would the plant be if it were built in the arctic where the low temperature reservoir is at 250k? Why don't we build all power plants in the arctic?

Answer 1

The "maximum possible efficiency" \[\eta_{\mbox{max}}\] is given by Carnot's theorem, which states that\[\eta_{\mbox{max}} = 1 - \frac{T_C}{T_H}\]where\[T_C\]is the "cold" temperature and \[T_H\]the "hot" temperature (both given in Kelvin). Using this formula, the maximum possible efficiency at the first situation is\[1 - \frac{300}{600} = 1 - \frac{1}{2} = \frac{1}{2}\]and for the second situation is\[1-\frac{250}{600} = \frac{7}{12} > \frac{1}{2}.\]