Solve the following problems An inventor claims that he deve

Solve the following problems: An inventor claims that he developed a heat engine operating between 300 degree C (highest temperature) and 15 degree C (lowest temperature) with thermal efficiency of 60%. Determine the maximum possible thermal efficiency if the engine is reversible. Is the heat engine possible or impossible? Why? An engineer A has considered developing a refrigerator using two temperature reservoirs in 90 degree F and 40 degree F. What is the maximum coefficient of performance (beta_max) if the refrigerator is reversible? An engineer B has considered developing a heat pump using two temperature reservoirs in 90 degree F and 40 degree F. What is the maximum coefficient of performance (Y_max) if the heat pump is reversible?

Solution

By Carnot\'s theorem, the thermal efficiency of a reversible cycle engine which cannot be exceeded

is given by

n_max= T1-T2/ T1=573-288/573 =0.497= 49.7%

n_{act =} 60%

Since actual efficiency is more than the maximum obtainable, the inventor\'s claim is infeasible not possible.

2.

cop of refrigerator ₌ T_cold/ T_hot-T_cold

Relation: C = F-32/ 1.8

T1 = 90-32/1.8 = 58/1.8 = 32.22 C= 305 k

T2= 40-32/1.8 = 4.44 C = 277 k

COP = 277/ 305-277 = 9.8

3.

Relation: C = F-32/ 1.8

T1 = 90-32/1.8 = 58/1.8 = 32.22 C= 305 k

T2= 40-32/1.8 = 4.44 C = 277 k

COP = 305/ 305-277 = 10.8

Note :cop of heat pump = cop ref +1