Calculate the cold reservoir temperature of a steam engine that uses hot steam at $450^{\circ }\text{C}$ and has a Carnot efficiency of 0.700. (b) What is unreasonable about the temperature? (c) Which premise is unreasonable?

Video Transcript

This is College Physics Answers with Shaun Dychko. We suppose hypothetically that a steam engine has a Carnot efficiency of 0.700 and a steam temperature of 450 degrees Celsius which is 723.15 Kelvin. We are gonna calculate the temperature of the cold reservoir by saying that the Carnot efficiency is 1 minus the T c divided by the T h. So we'll add T c over T h to both sides and subtract Eff c from both sides and this works out to T c over T h equals 1 minus Eff c. And then we'll multiply both sides by T h and we get that the T c then is the T h times 1 minus Eff c. So that's 723.15 Kelvin times 1 minus 0.700 which is 216.945 Kelvin which is minus 56.2 degrees Celsius. There are very few places on Earth's surface that are such low temperatures as this— only Antarctica only certain times of the year would have that temperature— so this steam engine would be unusable most of the time most places. It's unreasonable to presume a Carnot efficiency so high as 0.700.