You need an AC unit that transfers heat from your house at a

You need an AC unit that transfers heat from your house at a rate of 750 kJ/min to maintain its temperature at 22C when the outdoor air temperature is 45C. Your new, expensive unit operates on the reversed Carnot cycle! How much would it cost you to run this impossible machine for 24 hours if the price of a kW-h is KD0.030? (Check: answer between 0.700 and 0.801).

Solution

>> So, our unit works as a refrigerator and workes on Reversed Carnot Cycle

>> Now, Heat to be removed from room, Q2 = 750 kJ/min = 12.5 kW

>> T1 = Surrounding Temperature = 45 C = 318 K

>> T2 = Room Temperature = 22 C = 295 K

>> Now, Let Work Required to run this machine = W\" = ?

As, COP = Q2/W

and as it runs on reversed Carnot Cycle,

COP = T2/(T1 - T2)

=> Q2/W\" = T2/(T1 - T2)

=> 12.5/W\" = 295/(23)

=> Work Require = 0.975 kW

In a Day, Work Require = 0.975*4*60*60 = 84203.39 kW-h

As Price of a KW-h = KD 0.030

So, here, Total cost will be = 84203.39*0.030 = KD 2526.10 ............ANSWER.....