A Carnot engine’s operating temperatures are $210 ^\circ \textrm{C}$ and $45 ^\circ \textrm{C}$. The engine’s power output is 910 W. Calculate the rate of heat output.

VIDEO TRANSCRIPT

This is Giancoli Answers with Mr. Dychko. Efficiency is one minus the low temperature divided by high temperature for Carnot engine and that's one minus 45 degrees Celsius low temperature plus 273 to converted into Kelvin divided by 210 degrees Celsius plus 273 which is an efficiency of 0.34161 and the efficiency is the power output divided by the power input. You could say and we can solve this for Pin by multiplying both sides by Pin and over efficiency and on the left side it becomes Pin because efficiency is canceled and on the right side the Pin cancels and left with Pout over efficiency to the power output as 910 Watts divided by 0.34161 efficiency which gives us power input of 2663.856 watts now the rate of heat output is the difference between the input minus the power output and so this is the waste into the waste is the difference between what you put in versus what you get out and so we take this 2663 watts minus 910 Watts power output we're told and this gives us about 1800 watts of heat output.