A heat engine does 27776 J of work per cycle while exhaustin

A heat engine does 277.76 J of work per cycle while exhausting 616.53 J of heat to the cold reservior. If a Carnot engine operating with a hot reservior temperature of 566.45 ^oC has the same efficiency, what is the cold reservior temperature in degrees Celsius?

Solution

The heat engine is exhausting heat of Qc = 616.53 J to the cold sink while delivering a work per cycle of W = 277.76 J

Now, we know that the efficiency of a heat engine is given as: = 1 - Qc / Qh where Qh is the energy from the heat source. Also, we know that Qh = W + Qc = 894.29 J

Hence, efficiency = = 1 - 616.53 / 894.29 = 0.3106

Now, the carnot engine we have has the same efficiency, and for the carnot engines, we know that the efficiency is given as: = 1 - Tc / Th

That is, 0.3106 = 1 - Tc / 566.45

or, Tc / 566.45 = 0.6894

or, Tc = 390.51063 degree celsius.

Therefore the required temperature of the cold sink is 390.51063 degree celsius.