**Heat Pumps and Home Heating: An Educational Overview**A heat engine running backward is called a refrigerator if its purpose is to extract heat from a cold reservoir. The same engine running backward is called a **heat pump** if its purpose is to exhaust warm air into the hot reservoir. Heat pumps are widely used for home heating.You can think of a heat pump as a refrigerator that is cooling the already cold outdoors and, with its exhaust heat \( Q_H \), warming the indoors. Perhaps this seems a little silly, but consider the following: Electricity can be directly used to heat a home by passing an electric current through a heating coil. This is a direct, 100% conversion of work to heat. That is, 19.0 kW of electric power (generated by doing work at the rate 19.0 \( \text{kJ/s} \) at the power plant) produces heat energy inside the home at a rate of 19.0 \( \text{kJ/s} \).Suppose that the neighbor's home has a heat pump with a coefficient of performance of 3.00, a realistic value. **NOTE**: With a refrigerator, "what you get" is heat removed. But with a heat pump, "what you get" is heat delivered. So the coefficient of performance of a heat pump is\[ K = \frac{Q_H}{W_{in}}. \]An average price for electricity is about 40 \( \text{MJ} \) per dollar. A furnace or heat pump will run typically 250 hours per month during the winter.---This educational content explains the concept and application of heat pumps in home heating. It contrasts the direct conversion of electricity to heat in traditional heating systems with the more efficient heat transfer process in heat pumps. Understanding the coefficient of performance is crucial for evaluating the efficiency of heat pumps. **Question:**What does one month's heating cost in the home of a neighbor who uses a heat pump to provide the same amount of heating?*Express your answer in dollars.*

Name: **Heat Pumps and Home Heating: An Educational Overview**A heat engine
Uploaded: 2024-03-20T06:56:46.000Z
Channel: Bartleby
Description: **Heat Pumps and Home Heating: An Educational Overview**A heat engine running backward is called a refrigerator if its purpose is to extract heat from a cold reservoir. The same engine running backward is called a **heat pump** if its purpose is to