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Chapter 5: Problem 29

The chapter banner image (page 68 ) has two panels relating to the same hot water heater. One indicates the rate of gas usage when the heater is on (ignited, heating water) as \(40,000 \mathrm{Btu} / \mathrm{hr}\), and the other anticipates 242 Therms per year will be used. How many hours per day is the heater expected to be on (heating water) based on these numbers?

Short Answer

Expert verified
Answer: The heater is expected to be on for approximately 1.66 hours per day.

Step by step solution

01

Convert the Therms to Btu

To convert the Therms per year to Btu, we need to use the conversion factor: 1 Therm = 100,000 Btu. So, we have: 242 Therms/year * 100,000 Btu/Therm = 24,200,000 Btu/year
02

Calculate the total hours the heater is on in a year

We know the rate of gas usage when the heater is on is 40,000 Btu/hr. So, to find the total hours it is on in a year, we will divide the total Btu consumption by the rate of gas usage: Total Hours = (Total Btu consumption) / (Rate of gas usage) Total Hours = 24,200,000 Btu/year / 40,000 Btu/hr = 605 hours/year
03

Calculate the average hours per day the heater is on

Now, we need to find out how many hours per day the heater is expected to be on. To do this, we will divide the total hours in a year (605 hours) by the number of days in a year (365 days): Hours per day = (Total Hours) / (Number of days in a year) Hours per day = 605 hours/year / 365 days/year = 1.6575 hours/day The heater is expected to be on for approximately 1.66 hours per day.

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Most popular questions from this chapter

The numbers in Table \(5.1\) are reasonable but should not be thought of as right. \(^{40}\) You can make your own table by using \(m g h\) for lifting and \(\frac{1}{2} m v^{2}\) for kinetic energy. For this exercise, pick three familiar activities or situations that allow you to estimate an energy scale in Joules and compute/estimate the results.

If a microwave operates at a power of \(1,600 \mathrm{~W}(1,600 \mathrm{~J} / \mathrm{s})\), how long will it take to heat \(0.25 \mathrm{~L}\) of water from room temperature to boiling (changing temperature by \(80^{\circ} \mathrm{C}\) ) if \(50 \%\) of the microwave energy is absorbed by the water?

A typical textbook may have a mass of \(1 \mathrm{~kg}\), and thus a weight of about \(10 \mathrm{~N}\). How high could the textbook be lifted (against the force of gravity) by supplying one Joule of energy?

A smaller or less active person may require only \(1,300 \mathrm{kcal}\) per day of food intake, while a larger or more active person might demand \(3,000 \mathrm{kcal}\) per day. Approximately what range of power does this spread translate to, in Watts?

If a typical metabolic intake is \(2,000 \mathrm{kcal}\) each day, approximately how much energy does this translate to for one day, in units of \(\mathrm{kWh}\) ? Compare this to a typical American household's electricity usage of \(30 \mathrm{kWh}\) in a day.
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