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Chapter 15: Problem 15

A heat pump delivers heat at a rate of \(7.81 \mathrm{kW}\) for $10.0 \mathrm{h} .\( If its coefficient of performance is \)6.85,$ how much heat is taken from the cold reservoir during that time?

Short Answer

Expert verified
Answer: Approximately 1,200.6 kWh.

Step by step solution

01

Determine the work input

The formula for the coefficient of performance (COP) of a heat pump is given by: COP = Q_H / W where, COP = Coefficient of performance (6.85) Q_H = Amount of heat delivered by the heat pump (7.81 kW) W = Work input Let's find the amount of work input, using this formula: W = Q_H / COP

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Most popular questions from this chapter

In a heat engine, 3.00 mol of a monatomic ideal gas, initially at 4.00 atm of pressure, undergoes an isothermal expansion, increasing its volume by a factor of 9.50 at a constant temperature of \(650.0 \mathrm{K} .\) The gas is then compressed at a constant pressure to its original volume. Finally, the pressure is increased at constant volume back to the original pressure. (a) Draw a \(P V\) diagram of this three-step heat engine. (b) For each step of this process, calculate the work done on the gas, the change in internal energy, and the heat transferred into the gas. (c) What is the efficiency of this engine?
The efficiency of an engine is \(0.21 .\) For every \(1.00 \mathrm{kJ}\) of heat absorbed by the engine, how much (a) net work is done by it and (b) heat is released by it?
For a more realistic estimate of the maximum coefficient of performance of a heat pump, assume that a heat pump takes in heat from outdoors at $10^{\circ} \mathrm{C}$ below the ambient outdoor temperature, to account for the temperature difference across its heat exchanger. Similarly, assume that the output must be \(10^{\circ} \mathrm{C}\) hotter than the house (which itself might be kept at \(20^{\circ} \mathrm{C}\) ) to make the heat flow into the house. Make a graph of the coefficient of performance of a reversible heat pump under these conditions as a function of outdoor temperature (from $\left.-15^{\circ} \mathrm{C} \text { to }+15^{\circ} \mathrm{C} \text { in } 5^{\circ} \mathrm{C} \text { increments }\right)$
An ideal gas is in contact with a heat reservoir so that it remains at a constant temperature of \(300.0 \mathrm{K}\). The gas is compressed from a volume of \(24.0 \mathrm{L}\) to a volume of 14.0 L. During the process, the mechanical device pushing the piston to compress the gas is found to expend \(5.00 \mathrm{kJ}\) of energy. How much heat flows between the heat reservoir and the gas and in what direction does the heat flow occur?
A reversible engine with an efficiency of \(30.0 \%\) has $T_{\mathrm{C}}=310.0 \mathrm{K} .\( (a) What is \)T_{\mathrm{H}} ?$ (b) How much heat is exhausted for every \(0.100 \mathrm{kJ}\) of work done?
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