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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
Yes, the human body can be theoretically considered as a heat engine. It operates between two temperature sources (itself and the environment), converts chemical energy into mechanical work, and dissipates the residual heat into the environment.

Step by step solution

01

Understanding the concept of a heat engine

A heat engine operates between two heat reservoirs which are at different temperature levels. It absorbs heat from the high temperature body, performs some work and releases the rest of the heat to the low temperature body. The efficiency of a heat engine, denoted by \(\eta\), is determined by the ratio of the mechanical work output to the heat energy input.
02

Examination of the human body's operation

The human body consumes chemical energy from food, converts a part of it into useful work, and the remaining energy is lost as heat which gets dissipated into the environment. The body temperature which remains nearly constant at \(37^o C\) can be considered as the high-temperature reservoir. The surrounding environment where the body heat is dissipated can be seen as the low-temperature reservoir.
03

Can the human body be considered as a heat engine?

Yes, the human body's functioning of converting chemical energy into work and heat is akin to the operation of a heat engine. However, there is a fundamental difference. In case of the body, the source of energy is chemical (from food), while a heat engine works on heat energy supplied directly. Despite this difference, the comparison helps illustrate thermodynamic principles and efficiency of energy conversion within the body.

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Most popular questions from this chapter

Problem 74 of Chapter 16 provided an approximate expression for the specific heat of copper at low absolute temperatures: \(c=31(T / 343 \mathrm{K})^{3} \mathrm{J} / \mathrm{kg} \cdot \mathrm{K} .\) Use this to find the entropy change when \(40 \mathrm{g}\) of copper are cooled from \(25 \mathrm{K}\) to \(10 \mathrm{K}\). Why is the change negative?

A reversible engine contains 0.20 mol of ideal monatomic gas, initially at \(600 \mathrm{K}\) and confined to \(2.0 \mathrm{L} .\) The gas undergoes the following cycle: Isothermal expansion to \(4.0 \mathrm{L}\) \(\cdot\) Isovolumic cooling to \(300 \mathrm{K}\) Isothermal compression to \(2.0 \mathrm{L}\) \(\cdot\) Isovolumic heating to \(600 \mathrm{K}\) (a) Calculate the net heat added during the cycle and the net work done. (b) Determine the engine's efficiency, defined as the ratio of the work done to the heat absorbed during the cycle.

Why do refrigerators and heat pumps have different definitions of COP?

It costs \(\$ 180\) to heat a house with electricity in a typical winter month. (Electric heat simply converts all the incoming electrical energy to heat.) What would the monthly heating bill be after switching to an electrically powered heat-pump system with \(\mathrm{COP}=3.1 ?\)

Energy is conserved, so why can't we recycle it as we do materials?
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