Find the inside temperature of the house.

Question

A heat pump supplies heat energy to a house at the rate of 140,000 kJ/h when the house is maintained at 25°C. Over a period of one month, the heat pump operates for 100 hours to transfer energy from a heat source outside the house to inside the house. Consider a heat pump receiving heat from two different outside energy sources. In one application the heat pump receives heat from the outside air at 0°C. In a second application the heat pump receives heat from a lake having a water temperature of 10°C. If electricity costs $0.105/kWh, determine the maximum money saved by using the lake water rather than the outside air as the outside energy source.

Answer 1

Question

Chapter 1, Problem 11P

To determine

Find the inside temperature of the house.

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A heat pump supplies heat energy to a house at the rate of 140,000 kJ/h when the house is maintained at 25°C. Over a period of one month, the heat pump operates for 100 hours to transfer energy from a heat source outside the house to inside the house. Consider a heat pump receiving heat from two different outside energy sources. In one application the heat pump receives heat from the outside air at 0°C. In a second application the heat pump receives heat from a lake having a water temperature of 10°C. If electricity costs $0.105/kWh, determine the maximum money saved by using the lake water rather than the outside air as the outside energy source.

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We have exposed 1 kg of water, 1 kg of brick, and 1 kg of concrete each to a heat source that puts out 100 J every second. Assuming that all of the supplied energy goes to each material and they were all initially at the same temperature, which one of these materials will have a greater temperature rise after 10 s? We can answer this question using Equation as shown . We will first look up the values of the specific heat for water, brick, and concrete, which are cwater = 4180 J⁄kg K, cbrick = 960 J⁄kg K and cconcrete = 880 J⁄kg K . Now applying as shown , Ethermal = mc(Tfinal Tinitial) to each situation, it should be clear that although each material has the same amount of mass and is exposed to the same amount of thermal energy, the concrete will experience a higher temperature rise because it has the lowest heat capacity value among the three given materials.