Question

Jome one claims hove disigned eat pam p that at slead o f o 6 w to a dd hea to the warm inside o fthe house on Rate 36 Tempetuse 2 c Power inpu 2 4 6 at side is 27o k and the warm insi te 213k. Cheq ck If the des汐n p ea sible or no by comparing λ and Amax

Answer 1

Let us assume a carnot heat pump b/w the 270K and 298K as given to maintain temperature of 293K inside house 3600w heat is added So Q_H = 3600 w for cannot heat pump Q_H/w_in = T_H/T_H - T_L = 293/293 - 270 so w_in = 3600 times 23/293 = 282.5938 w or 0.28259 kw so (COP)_max = Q_H/q_in = 3600/282.5938 = 12.7391 Above cop(coefficient of performance) is max because it is carnot heat pump so if cop for HP claimed by someone is greater than this (COP)max = than claim is false otherwise correct. So (COP)_claim = Q_H/w_in = 3600/0.6 times 10^3 = 6 as (COP)_claim < (COP)_max hence the design is fisible.