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Chapter 19: Problem 19

The human body can be \(25 \%\) efficient at converting chemical energy of fuel to mechanical work. Can the body be considered a heat engine, operating on the temperature difference between body temperature and the environment?

Short Answer

Expert verified
Though the human body exhibits some characteristics of a heat engine, it does not meet the strict criteria of one due to it not operating on the principle of temperature difference between two reservoirs. Therefore, it can't be considered a complete heat engine.

Step by step solution

01

Understand Efficiency of Energy Conversion

Efficiency refers to how much of the total energy is actually converted into useful work. The exercise mentions that the human body is \(25\%\) efficient at converting the chemical energy of food into mechanical work. But, the efficiency of a Carnot (also known as, a perfect heat) engine, is given by the formula \(1 - Tc/Th\), where \(Tc\) is the temperature of the cold reservoir and \(Th\) is the temperature of the hot reservoir. In our case, \(Th\) would be the body temperature and \(Tc\) would be the ambient temperature. Both temperatures should be measured in Kelvin.
02

Apply the Concept of a Heat Engine

A heat engine operates on the principle of converting heat energy into mechanical work due to the temperature difference between two reservoirs. Comparably, the human body appears to operate in a similar manner by converting the chemical energy in food (fuel) into mechanical work.
03

Conclude If the Human Body can be Considered a Heat Engine

While the human body has parallels with heat engines, such as the conversion of one energy form into another, it does not strictly adhere to the scientific definition of a heat engine. This is because external temperatures do not affect the efficiency of the human body's energy conversion whereas in a heat engine, efficiency strongly depends on the temperate difference between the heat source and heat sink.

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Most popular questions from this chapter

A reversible engine contains 0.350 mol of ideal monatomic gas, initially at \(586 \mathrm{K}\) and confined to a volume of \(2.42 \mathrm{L}\). The gas undergoes the following cycle: \(\bullet\) Isothermal expansion to \(4.84 \mathrm{L}\) \(\bullet\) Constant-volume cooling to \(292 \mathrm{K}\) \(\bullet\) Isothermal compression to \(2.42 \mathrm{L}\) Determine the engine's efficiency, defined as the ratio of the work done to the heat absorbed during the cycle. \(\bullet\) Constant-volume heating back to \(586 \mathrm{K}\)

Use energy-flow diagrams to show that the existence of a perfect heat engine would permit the construction of a perfect refrigerator, thus violating the Clausius statement of the second law.

The temperature of \(n\) moles of ideal gas is changed from \(T_{1}\) to \(T_{2}\) with pressure held constant. Show that the corresponding entropy change is \(\Delta S=n C_{p} \ln \left(T_{2} / T_{1}\right)\)

It costs \(\$ 230\) to heat a house with electricity in a winter month. (Electric heat converts all the incoming electrical energy to heat.) What would the monthly heating bill be after converting to an electrically powered heat pump with \(\mathrm{COP}=3.4 ?\)

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?
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