The exhaust temperature of a heat engine is $230 ^\circ \textrm{C}$. What is the high temperature if the Carnot efficiency is 34%?

VIDEO TRANSCRIPT

This is Giancoli Answers with Mister Dychko. Carnot efficiency is the ideal efficiency and it's one minus the low temperature reservoir divided by the temperature of the high temperature reservoir. We can rearrange this a little bit by taking this to the left hand side which makes it positive and then take this to the right hand side making it Tl over Th equal one minus efficiency. Then we can take the reciprocal of both sides so we raise both sides to the exponent negative one and that flips the left side. So, Th over Tl and the right hand side starts off as one minus e all over one and then when you flip it, it becomes one over one minus e. And then multiply both sides by T low and you get the high temperature is the low temperature divided by one minus e. The temperature always has to be in Kelvin so that's 230 degrees Celsius plus 273 to convert into Kelvin divided by one minus 0.34 and you get about 490 degrees Celsius after you subtract 273 away from this answer in Kelvin.