Chapter 5, Problem 5.36P

A Carnot heat pump is used to maintain the temperature inside a building at 20 ∘C. Significantly, the colder it gets outside, the more heat is lost through the walls and windows of the building. Assume that 45 kW of heat are lost for each degree difference between the outside and the inside temperature. That means that the colder it gets, the harder the heat pump will need to work. However, for safety reasons, the controller circuit for the heat pump limits its electrical power consumption to 195 kW. What's the coldest it can get outside before the heat pump can't maintain the building temperature adequately?

QI Two reservoirs 727 °C and 23 °C are used to operate heat engine. 50% from the power output of heat engine is employed to drive a reversed Carnot refrigerator that absorbs heat from the cooled space at -2 °C at a rate of 6.7 Kw and rejects heat to the surrounding at 200 °C. Calculate the rate of heat supplied to the heat engine.

A heat pump with a coefficient of performance of 3.5 provides energy at an average rate of 70,000 kJ/h to maintain a building at 20 deg C on a day when the outside temperature is -5 deg C. If electricity costs 8.5 cents per kWh, (a) determine the actual operating cost and the minimum theoretical operating cost, each in $/day. (b) compare the results of part (a) with the cost of electrical-resistance heating.

A heat pump cycle is used to maintain the interior of a building at 25°C. At steady state, the heat pump receives energy by heat transfer from well water at 9°C and discharges energy by heat transfer to the building at a rate of 120,000 kJ/h. Over a period of 14 days, an electric meter records that 1500 kW · h of electricity is provided to the heat pump.Determine:(a) the amount of energy that the heat pump receives over the 14-day period from the well water by heat transfer, in kJ.(b) the heat pump’s coefficient of performance.(c) the coefficient of performance of a reversible heat pump cycle operating between hot and cold reservoirs at 25°C and 9°C.

An air conditioner operating at steady state maintains a dwelling at 20°C on a day when the outside temperature is 40°C. Energy is removed by heat transfer from the dwelling at a rate of 3200 J/s while the air conditioner’s power input is 0.8 kW. Determine the coefficient of performance of the air conditioner. Determine the power input required by a reversible refrigeration cycle providing the same cooling effect while operating between hot and cold reservoirs at 40°C and 20°C, respectively, in kW.

A refrigerator operates at steady-state with a COP of 4.5 and power input of 0.8kW. If energy is rejected from the refrigerator to the surroundings at 20°C because of heat transfer from metal coils, the rate of energy rejection is computed as kW and the lowest theoretical temperature inside the refrigerator would be °C.

A heating system must maintain the interior of a building at TH = 20°C when the outside temperature is TC = 2°C. If the rate of heat transfer from the building through its walls and roof is 16.4 kW, determine the electrical power required, in kW, to heat the building using (a) electrical-resistance heating, (b) a heat pump whose coefficient of performance is 3.0, (c) a reversible heat pump operating between hot and cold reservoirs at 20°C and 2°C, respectively.

A heat pump maintains a dwelling at 68°F. When operating steadily, the power input to the heat pump is 3 hp, and the heat pump receives energy by heat transfer from 55°F well water at a rate of 500 Btu/min. (a) Determine the coefficient of performance. (b) Evaluating electricity at $0.18 per kW · h, determine the cost of electricity in a month when the heat pump operates for 300 hours.

A claim states that a heat pump has been invented that requires work to be done on the system of 400kJ and delivers energy to its surrounding by heat transfer of 300kJ. Such device is possible True False