Question

A mechanical engineer claims that he inspected a heat engine and found the following information. The heat engine receives heat from a heat source at 1200 oC and rejects heat to a heat sink at 500 oC. The heat engine produces 500 kJ of work and has a thermal efficiency of 40%. Is this heat engine possible? Why? Determine the heat supplied to this engine by the heat source. Determine the heat rejected to heat sink.

Answer 1

a) This heat engine is possible since real efficiency is lesser than theoretical efficiency, b)
`Q_(H) = 1250\,kJ`, c)
`Q_(L) = 750\,kJ`.

Step-by-step explanation:

a) The maximum theoretical efficiency of a heat efficiency is given by the Carnot's cycle, whose formula is:

`\eta_(max) = \left(1 - (773.15\,K)/(1473.15\,K)\right)* 100\,\%`

`\eta_(max) = 47.5\,\%`

This heat engine is possible since real efficiency is lesser than theoretical efficiency.

b) The heat supplied to the engine by the heat source:

`Q_(H) = (W)/(\eta_(real))`

`Q_(H) = (500\,kJ)/(0.4)`

`Q_(H) = 1250\,kJ`

c) The heat rejected to heat sink is:

`Q_(L) = Q_(H) - W`

`Q_(L) = 1250\,kJ - 500\,kJ`

`Q_(L) = 750\,kJ`