Question

When a man returns to his well-sealed house on a summer day, he finds that the house is at 35°C. He turns on the air conditioner, which cools the entire house to 20°C in 30 min. If the COP of the air-conditioning system is 2.8, determine the power drawn by the air conditioner. Assume the entire mass within the house is equivalent to 800 kg of air for which cv = 0.72 kJ/kg·°C and cp = 1.0 kJ/kg·°C.

Answer 1

`\dot W = 1.667\, kW`

Step-by-step explanation:

A well-sealed house means that there is no mass interaction between air indoors and outdoors. Hence, cooling process is isochoric. The heat removed by the air conditioner is:

`\dot Q_(L) = (m_(air))/(\Delta t) \cdot c_(v, air) \cdot (T_(o)-T_(f))\\\dot Q_(L) = (800\, kg)/((30\, min)\cdot ((60\, s)/(1 \, min) ))\cdot (0.7 (kJ)/(kg \cdot K)) \cdot (15\, K)\\\dot Q_(L) = 4.667\, kW`

The power drawn by the air conditioner is:

`\dot W = (\dot Q_(L))/(COP_(R)) \\\dot W = \frac {4.667\, kW}{2.8}\\\dot W = 1.667\, kW`