Electricity can be directly used to heat a home by passing an electric current t

Question

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, 15 kW of electric power ( generated by doing work at the rate 15 kJ/s at the power plant) produces heat energy inside the home at a rate of 15 kJ/s. Suppose that the neighbor's home has a heat pump with a coefficient of performance of 5.0.
a) How much electric power (in kW) does the heat pump use to deliver 15 kJ/s of heat energy to the house ?
b) An average price of electricity is about 40 MJ per dollar. A furnace or heat pump will run typically 200 hours per month during the winter. What does one month's heating cost in the home with a 15 kW electric heater and in the home of the neighbor who uses an equivalent heat pump?

Explanation / Answer

a) coff of performance= 5 = heta delivered / work input electric power required for heat pump = work input = 15( heat delivered )/ 5 = 3 kw b) cost with electric heater total energy for 200 hours = 15 * 200 =3mega joule 40 mega joule 1 dollar for 3 mega joule cost = 3/40 dollars cost with heat pump electric power require= work input = 3 kw otal energy for 200 hours= 3* 200 = 0.6 mega joule 40 mega joule 1 dollar for 0.6 mega joule cost= 0.6/40= 0.015 dollar

Related Questions

Navigate

• Browse (All)
• Browse E
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.