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Chapter 19: Problem 5

Your power company claims that electric heat is \(100 \%\) efficient. Discuss.

Short Answer

Expert verified
Electric heaters are usually deemed '100% efficient' since every bit of the electrical energy they employ is eventually transformed into heat. This however only considers the conversion of electricity to heat, not accounting for any lost energy in sound or light, or energy used up for non-heating functions of the device.

Step by step solution

01

Understanding energy efficiency

Efficiency is defined as the ratio of useful energy output to the total energy input, expressed in a percentage form. In the context of an electric heater, the electrical energy (input energy) is expected to be converted entirely to thermal energy (output energy).
02

Considering energy losses

In a real scenario, there are always energy losses especially in the form of sound, light or other forms of energy. In the context of an electric heater, there could be energy loss in the resistance wires, connectors, or even in the heat transferred to the parts of the heater which isn't used to heat the room.
03

Energy Conversion

Despite the losses, in terms of energy conversion, electric heaters are considered '100% efficient' because all of the electric energy they consume is eventually converted into heat energy. However, this statistic doesn't consider any other non-heat related function the device is performing. If we consider these, the efficiency would no longer be 100%.

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Most popular questions from this chapter

A box containing 10 coins lying heads up is found to have only 5 coins heads up after shaking. Is there any positive entropy change?

A cosmic heat engine might operate between the Sun's \(5800 \mathrm{~K}\) surface and the \(2.7 \mathrm{~K}\) temperature of intergalactic space. What would be its maximum efficiency?

Could you cool the kitchen by leaving the refrigerator open? Explain.

(a) Continue the calculation begun on page 372 in the subsection "Irreversible Heat Transfer" to derive the expression given in the text for the entropy change when equal masses \(m\) of hot and cold water, at temperatures \(T_{\mathrm{h}}\) and \(T_{c}\), respectively, are mixed: \(\Delta S=m c \ln \left[\left(T_{c}+T_{\mathrm{h}}\right)^{2} / 4 T_{\mathrm{c}} T_{\mathrm{h}}\right]\). (b) Show that the argument of the logarithm in this expression is greater than 1 for \(T_{\mathrm{h}} \neq T_{c}\), thus showing that \(\Delta S\) is positive. Hint: This is equivalent to showing that \(\left(T_{c}+T_{\mathrm{h}}\right)^{2}>4 T_{\mathrm{c}} T_{\mathrm{h}}\). Expand the left side of this inequality, subtract \(4 T_{\mathrm{c}} T_{\mathrm{h}}\) from both sides, factor the resulting left side, and you'll have your result.

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