Topic: Thermodynamics
A room contains 25 kg of air at 100 kPa and $14^{\circ}C$ The room has a 250 W refrigerator and 1 kW electric resistance heater. During a cold winter day, it is observed that both the refrigerator and the heater are running continuously, but the air temperature in the room remains constant. The rate of heat loss from the room during that day is
- A. $3600~kJ/hr.$
- B. $1250~kJ/hr.$
- C. $4500~kJ/hr.$
- D. $2700~kJ/hr.$
Answer: C. $4500~kJ/hr.$
Explanation: Since the air temperature in the room remains constant, the total heat added to the room must equal the heat loss to the surroundings. The power consumed by both the refrigerator (250 W) and the heater (1 kW = 1000 W) acts as heat input to the room. Total heat input $H_{in} = 250 + 1000 = 1250~W = 1250~J/s$. Rate of heat loss = $1250 \times 3600~J/hr = 4.5\times10^{6}~J/hr = 4500~kJ/hr$.