Electrical Energy

Electrical energy is undoubtedly the primary source of energy consumption in any modern household. Most electrical energy is supplied by commercial power plants. The most common poswer plants are fueled by coal, oil, or nuclear fuel. But there are hydroelectric power plants that capture the power of falling water, geothermal plants that use the heat from beneath the earths crust, and wind farms that capture the energy of wind. And finally, electrical power from solar radiation is steadily gaining ground. We will deal with electricity from solar energy in the next section.

Common Household Appliances

In this section we will consider some of the major appliances that consume most of the electrical energy in a household. The propane stove is covered in the Chemical Energy section of this module.

Conventional Electric Stove

The conventional electric stove operates in on a principle we have already studied in detail. Electrical energy is converted to heat energy in the resistive "elements" of the stove. One of the differences between a stove element and an incandescent light bulb is the operating temperature. While the light bulb operates at a very high temperature in order to produce visible light, the stove element is designed to operate at a lower temperature. At the highest setting, most elements glow a dull red. The element temperature is still very high, much higher than the temperature at which the food itself cooks. But this higher temperature is necessary to keep heat energy flowing into the food. For the top side elements, heat reaches the food through conduction. In the oven, convection is the primary method of heating the food.

Since the light bulb glows white hot, does it consume more energy than the dull red stove element? Typical 6" coil-type stove top elements consume about 1500 W at the high setting, far more than any single light bulb. They are able to produce more heat at a lower temperature because the surface area of the coils are far greater than the surface area of the bulb filaments.

Microwave Oven

The microwave oven operates very differently from a conventional oven. It heats through radiation. The microwave oven produces microwaves, which are electromagnetic waves just like light, but at a lower frequency (the GHz range!). The microwaves penetrate and are absorbed by the molecules of the food. It is primarily the water molecules that absorb the energy, but fat molecules absorb as well. Mechanically, you can visualize the alternating electric field of the microwaves as rotating the water molecule back and forth, creating thermal energy.

The alternating electric field is able to exert forces on the water molecule because it is polar and free to rotate. You may know from experience, that microwaves don't heat common container materials such as plastics and ceramics. But you may be suprised to know that ice does not microwave very well. Not at first, anyway. The H₂O molecules are held rigidly in place. But once the ice begins to melt, the regions that have become water begin absorbing energy and melting the surrounding area. A mid-sized microwave oven consumes about 1000 W and is a bit more efficient than the conventional oven in converting electrical energy to heat energy. If you would like to know more, check out the Special Projects link on Microwave Ovens.

Water Heater

The basic design of the standard water heater hasn't changed much in the last few decades. Heating elements are usually located near the bottom and middle of a tank of water. (Small units usually have only one heating element.) Heat from the coils are transferred to the water immediately surrounding the coils through both direct conduction and to a lessor degree, radiation. However, this heat is spread out through convection. As the water around a coil increases in temperature, it expands and becomes less dense. It rises upward and colder water moves in to take its place. A convection cell is created within the heater tank. Insulation is a subject important to an efficient water heater. Most of the time, hot water is held in the tank, ready to be used upon demand. To maintain the desired temperature, the minimum energy supplied by the coil must match the heat energy conducted into the cooler surrounding environment. The better insulated the tank, the smaller the losses. (Many households place a timer on the water heater that turn it off during the day when no one is at home.) A typical water heater consumes about 2000 W when operating. How often it operates is a function of both water usage and heat losses. The California Energy Commission provides a nice site which discusses important energy considerations for choosing a water heater. For more details on the operation of the water tank, check out How the Hot Water Heater Works from the How Stuff Works website.

Refrigerator

The refrigerator is essentially a heat pump. Heat is removed from the inside of the refrigerator and pumped to the outside. The method is a combination of adiabatic cooling and evaporation inside the fridge and a combination of radiative and convective cooling outside the fridge.

The refrigeration system consists of a working gas/liquid (called the refrigerant), a compressor, an external coiled or snaking pipe (often called the condensor coil), and an internal pipe (often called the expansion coil). The refrigerant is normally a gas at room temperture, but can be liquified at high pressures. The compressor compresses the gas and forces into the condensor coil outside the fridge. The compressed gas is hot. As the gas makes it way through the outside coil it cools. Essentially, the heat is removed by radiation and convection. Place your hand on or near the coils at the back of the fridge and you can feel the radiated heat. Manufacturer's instructions ususally recommend a minumum clearance so that cooler air can circulate over the coils to help increase convective cooling. By the time the refrigerant makes it through the condensor, enough heat has been removed to make it partially liquid. It is now ready to enter the coils inside the fridge.

The cooled high pressure liquid refrigerant is force through an expansion valve into the lower pressure evaporation coil on the inside of the fridge. The refrigerant expands and evaporates in the lower pressure and the combination of adiabatic expansion and evaporative cooling lowers the temperature of the refrigerant considerably. The evaporation coils become very cold and absorb heat from the inside of the fridge. At the far end of the evaporation coils the refrigerant enters the compressor and the cycle starts over.

For a more detailed diagram of the refrigerator, visit Princeton University's "active zone" refrigerator diagram.

Water Pump

The water pump is a crucial element to most residents of the Caribbean, and to any household not connected to a public system. As was done in the Plumbing module, the water pump can be viewed in terms of the pressure it must create to lift water from the cistern to the plumbing fixtures. But we can understand the task it performs in terms of energy as well. The pump does three things energetically. It must

1. increase the height of the water,
2. it must accelerate it from rest (in the cistern) to the flow velocity at the faucet,
3. and it must overcome frictional losses in the pipes.

Let's consider the first two items. Recall the definitions of work and energy from the first module. The work done by a force is the force times the distance over which the force acts. The water pump must exert a force equal to the weight of the water to lift it up a distance equal to the height. That is, to raise a mass m of water to a height h, the work is

This energy associated with height is also called gravitational potential energy. The pump must also give the water kinetic energy. This is the energy associated with motion. The water has no kinetic energy in the cistern, but it certainly has kinetic energy leaving the faucet. The kinetic energy (KE) of a mass m with speed v is given by,

As with all electical devices, we must think of the power the pump supplies, not just energy. The pump must raise and accelerate a certain mass of water per unit time. So let's estimate what our water pump must do. Assume a faucet is located 3 m above the water level of the cistern. (This is a reasonable estimate for a one-story home with a nearly empty cistern.) Assume that we would like the faucet to supply 1 liter (that's 1 kg!) in 10 seconds. (That's just over a gallon/minute.) The change in height is easy, its 3 m. To find the velocity, we need to use the flow rate equation, Flow Rate = Av. The flow rate is 1 liter/10 seconds = 10^-4 m³/s. Most faucets are supplied with ¹/₂" pipe, that's a diameter of 1.27 cm. The area A would be A = p(.0127/2)² = 1.27 x 10^-4m². Solving, 10^-4 = 1.27 x 10^-4 v, we get v = .79 m/s. The total energy the pump must supply to 1 kg of water would be

It's worth noting that almost all of the energy is contained in the PE term. In other words, most of the energy is expended to lift the water.

The power supplied by the pump is Power = Work/time = 30 J/10 s = 3 Watts. Most pumps, designed for single story homes, are rated at ¹/₄ to ¹/₂ hp. This is 190 to 370 Watts. It may seem that this far exceeds what is needed. In fact it is usually quite adequate, but don't forget we calculated the minimum for only one faucet. In practice, there can be many spigots opened at once.

And we did not consider the last item in our list, frictional losses. The frictional losses are much more difficult to calculate. We would need to know the diameters and lengths of the pipes (remember Poiseuille's equation?) and how many bends and joints are in the system. Frictional losses typically account for the majority of the total power consumption in one and two story homes.

Paying for Energy

Here in the VI, when the Water and Power Authority (WAPA) bill arrives, you have to pay for the electrical energy you consumed that month. You do not pay for the power! The power is the rate of your energy consumption and varies throughout the month. As before, the energy is related to the power by

Although energy is measured in Joules, you will not these units on the bill. In just one hour, a single 100 W light bulb will consume a total of 100 Joules /sec x 3600 sec = 360, 000 Joules! That's a lot of Joules. Power companies use a more reasonably sized unit for power call the "kilowatt hour", denoted "kWhr". It's very easy to understand.

That is, 1 kW x 1 hr = 1 kWhr. (That's 3.6 million Joules!) The cost of electricity varies considerably around the world. It is a function of the cost of fuel to run the power plant (such as oil, coal, and nuclear fuel) and the construction cost of the plant. The average cost here in the VI is roughly 19 cents per kWhr. The VI rates are determined by a rather complicated scheme that includes the cost of public lighting, waste heat recovery boiler, etc. In the summer of 2003, WAPA published a Rate Comparison Chart that gives a flavor of these charges.

Problem: Let's consider the 1200 W hairdryer in the previous problem set. How much does it cost per month if you use it everyday for 15 minutes?

Solution: We want the number of kW times the number of hours to find the energy in kWhr. Converting to kW, we know 1200 W is 1.2 kW. The total time per month is about 15 min/day x 30 days/month = 450 minutes/month = 450/60 = 7.5 hrs/month. So the energy used is 1.2 kW x 7.5 hrs = 9.0 kWhr. The cost would be 9.0 kWhr x .15 dollars/kWhr = $ 1.35.

Problem: A refridgerator rated at 1000 W operates one third of time. What does it cost per month? Assume 15 cents/ kWhr.

Solution:1000 W = 1.0 kW. The number of hours that the fridge is running is ¹/₃ x 24 hrs/day x 30 days/240 month = 240 hr. So, cost = 1 kW x 240 hr x $.15 /kWhr = $36. An energy saving refrigerator that runs only 25% of the time would cost $27 per month, saving $9 every month or over $100 per year.

If your are interested in the energy consumption of a particular appliance, the US Department of Energy provides a list of energy consumption for many common household appliances. (cached version)

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