An engineer claims to have measured the characteristics of a

An engineer claims to have measured the characteristics of a heat engine that takes in 130 J of thermal energy and produces 50 J of useful work. What is the smallest possible ratio of the temperatures (in kelvin) of the hot and cold reservoirs? Express your answer using two significant figures. 4H=

Solution

efficiency of heat engine () = Work done / heat supplied = 50 / 130

   = 5/13

so efficiency is also related this way () = 1-T_cold/T_hot

5/13 = 1- T_cold/T_hot

T_cold/T_hot = 1 - 5/13 = 8/13 = 0.615

so T_hot/.T_cold = 1 / 0.615 = 1.625