OpenStax College Physics, Chapter 15, Problem 28 (Problems & Exercises)

This is College Physics Answers with Shaun Dychko. An engine has an efficiency of 30.0 percent and it has a cold temperature reservoir that it expels heat to at a temperature of 200 degrees Celsius. We are gonna convert this into Kelvin by adding 273.15 and we are gonna assume that this is the efficiency of a Carnot engine and the question is what is the temperature of the high temperature reservoir in this scenario? So we'll add T c over T h to both sides and our job is to solve for T h and then subtract efficiency Carnot from both sides and this makes zero on the left and then T c over T h is gonna remain on the left here and the right hand side will have 1 minus Eff c. And then multiply both sides by T h to get it out of the denominator and switch the sides around and we have T h times 1 minus Eff c equals T c and then divide both sides by 1 minus Eff c and we get that the high temperature reservoir is the cold temperature reservoir divided by 1 minus Eff c. So that's 473.15 Kelvin divided by 1 minus 0.300 which is 676 Kelvin and since the question gave us the original temperature in degrees Celsius, let's assume that they want the final answer in degrees Celsius as well. So the high temperature reservoir has a temperature of 403 degrees Celsius given a Carnot efficiency of 30.0 percent and a cold temperature reservoir of 200 degrees Celsius.