Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 19: Problem 37

You operate a store that's heated by an oil furnace supplying 30 kWh of heat from each gallon of oil. You're considering switching to a heat-pump system. Oil costs \(\$ 1.75 /\) gallon, and electricity costs \(16.5 \notin / \mathrm{kWh} .\) What's the minimum heat-pump COP that will reduce your heating costs?

Short Answer

Expert verified
The minimum COP for the heat pump to be cost-effective as compared to the oil furnace is 283.17.

Step by step solution

01

Calculate the Oil Furnace Efficiency

The oil furnace supplies 30 kWh of heat from each gallon of oil. So, for each dollar spent on oil, the system produces \(30 kWh / 1.75 $ = 17.14 kWh/$\).
02

Calculate Electricity Costs

Next, calculate how much heat can be obtained per dollar from electricity. This will be \(1 kWh / 16.5 $ = 0.0606 kWh/$\), based on the given electricity cost.
03

Calculate Minimum Heat-Pump COP

The heat pump has to be at least as efficient as the oil furnace, that means the COP must be the ratio between the efficiency of the oil furnace and the cost of the electricity, or COP = \(17.14 kWh/$ / 0.0606 kWh/$ = 283.17\). This is the minimum COP for the heat pump to be as cost-effective as the oil furnace.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

In an alternative universe, you've got the impossible: an infinite heat reservoir, containing infinite energy at temperature \(T_{\mathrm{h}} .\) But you've only got a finite cool reservoir, with initial temperature \(T_{\mathrm{c} 0}\) and heat capacity \(C .\) Find an expression for the maximum work you can extract if you operate an engine between these two reservoirs.

Refrigerators remain among the greatest consumers of electrical energy in most homes, although mandated efficiency standards have decreased their energy consumption by some \(80 \%\) in the past four decades. In the course of a day, one kitchen refrigerator removes \(30 \mathrm{MJ}\) of energy from its contents, in the process consuming \(10 \mathrm{MJ}\) of electrical energy. The electricity comes from a \(40 \%\) efficient coal-fired power plant. The fuel energy consumed at the power plant to run this refrigerator for the day is a. \(12 \mathrm{MJ}\). b. \(25 \mathrm{MJ}\). c. \(40 \mathrm{MJ}\). d. \(75 \mathrm{MJ}\).

Why doesn't the evolution of human civilization violate the second law of thermodynamics?

A Carnot engine absorbs \(900 \mathrm{J}\) of heat each cycle and provides \(350 \mathrm{J}\) of work. (a) What's its efficiency? (b) How much heat is rejected each cycle? (c) If the engine rejects heat at \(10^{\circ} \mathrm{C},\) what's its maximum temperature?

An ideal gas undergoes a process that takes it from pressure \(p_{1}\) and volume \(V_{1}\) to \(p_{2}\) and \(V_{2},\) such that \(p_{1} V_{1}^{\gamma}=p_{2} V_{2}^{\gamma},\) where \(\gamma\) is the specific heat ratio. Find the entropy change if the process consists of constant-pressure and constant-volume segments. Why does your result make sense?
See all solutions

Recommended explanations on Physics Textbooks

Work Energy and Power

Read Explanation

Translational Dynamics

Read Explanation

Electricity

Read Explanation

Fundamentals of Physics

Read Explanation

Solid State Physics

Read Explanation

Medical Physics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free