Physics chapter 4 #11

Question

A heat engine does 300 J of work per cycle while exhausting 700 J of heat to the cold reservoir. What is the engine's thermal efficiency?

A Carnot engine with a hot-reservoir temperature of 410 degrees C has the same thermal efficiency. What is the cold-reservoir temperature in degrees C?

Answer 1

Thermal efficiency

= work done / total heat used x 100 percent

= 300 / (300+700) x 100 percent

= 30 percent.

Hot reservoir temperature = 410 + 273 = 683 K

If T = cold reservoir temperature in K, then

30 = (683 - T) x 100 / 683

=> 100T = 68300 - 30 * 683 = 47810

=> T = 478 K

= 478 - 273 degree C

= 205 degree C.