Question

A certain heat engine operates between 1000K and 500K (a) what is the maximum efficiency of the engine? (b) calculate the maximum work that can be done by for each 1.0 kJ of heat supplied by the hot source. (c) how much heat is discharged into the cold sink in a reversible process for each 1.0 kJ supplied by the hot source?

Answer 1

(a) The maximum efficiency of a heat engine is given by the formula:

Efficiency = 1 - (Tc/Th)

where Tc is the temperature of the cold reservoir and Th is the temperature of the hot reservoir. Plugging in the values, we get:

Efficiency = 1 - (500/1000) = 1 - 0.5 = 0.5 or 50%

Therefore, the maximum efficiency of the engine is 50%.

(b) The maximum work that can be done by the engine for each 1.0 kJ of heat supplied by the hot source is given by the formula:

Maximum work = Efficiency * Heat supplied

Plugging in the values, we get:

Maximum work = 0.5 * 1.0 kJ = 0.5 kJ

Therefore, the maximum work that can be done by the engine for each 1.0 kJ of heat supplied is 0.5 kJ.

(c) The amount of heat discharged into the cold reservoir in a reversible process for each 1.0 kJ supplied by the hot source can be calculated by using the formula:

Heat discharged = Heat supplied - Maximum work

Plugging in the values, we get:

Heat discharged = 1.0 kJ - 0.5 kJ = 0.5 kJ

Therefore, for each 1.0 kJ supplied by the hot source, 0.5 kJ is discharged into the cold reservoir in a reversible process.