Question

An inventor claims to have developed a heat pump that produces a 200-kW heating effect for a 293 K heatedzone while only using 75 kW of power and a heat source at 273 K. Justify the validity of this claim.

Answer 1

From the calculation, we can see that the invention's COP of 2.67 does not exceed the maximum theoretical COP of 14.65. Hence his claim is valid and could be possible.

Step-by-step explanation:

Heat generated Q = 200 kW

power input W = 75 kW

Temperature of heated region
`T_(h)` = 293 K

Temperature of heat source
`T_(c)` = 273 K

For this engine,

coefficient of performance COP = Q/W = 200/75 = 2.67

The maximum theoretical COP obtainable for a heat pump is given as

COP =
`(T_(h) )/(T_(h) - T_(c) )` =
`(293 )/(293 - 273 )` = 14.65

From the calculation, we can see that the invention's COP of 2.67 does not exceed the maximum theoretical COP of 14.65. Hence his claim is valid and could be possible.