Question

S. In Nashville, on a particular summer day, assume that you want the inside temperature at 23 Co the outside temperature is 43 Co. In Chicago, a outside temperature is 30 C Using a Carnot refrigerator as a limit, tell in which location will you get the most bang for your buck (heat transferred per unit energy expended). In your answer be both quantitative and qualitative.

Answer 1

In Inside temperature = 23 c + 273 = 296 k outside temperature = 43 c + 273 = 316 k In Chicago Inside temperature = 30 + 273 = 303 k using cannot air Refrigerator as a limit we can say that cop cannot cycle depends on temperature only Q_2 is the heat extracted from low temp area w is work supplied let here T, be inside temp and T_2 be outside temperature iR Nashville cop = T_2/T_1 - T_2 = 296/316 - 296 = 14.8 cop = 14.8 in Chicago cop = T_2/T_1 - T_2 = 296/303 - 296 = 42.2 cop = 42.2 cop is coefficient of per unit work input = Q_2/w = in this case cop for Chicago is more than Nashville therefore we have get more bang in Chicago