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During cycling, the human body typically releases stored energy from food at the rate of \(500 \mathrm{W},\) and produces about \(120 \mathrm{W}\) of mechanical power. At what rate does the body produce heat during cycling?

Short Answer

Expert verified
The body produces heat at a rate of \(380 \mathrm{W}\) during cycling.

Step by step solution

01

Identify given quantities

The energy released by the human body is given as \(500 W\). The mechanical power produced by the body is given as \(120 W\).
02

Understand the problem

The body consums energy stored from food when cycling. However, only a fraction of this energy is transformed into useful mechanical power. The rest of the energy is released as heat because the human body is not 100% efficient.
03

Calculate the rate at which heat is produced

Subtract the mechanical power produced from the total energy released to find the heat produced. This is based on the energy conservation principle, which means all energy used will come out as either useful power or heat. So, the heat produced (\(P_{heat}\)) can be calculated as: \[P_{heat} = P_{total} - P_{mech} = 500 W - 120 W = 380 W\]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Energy Transformation
Energy transformation is a fundamental concept in physics which refers to the process of converting one form of energy into another. For students tackling exercises about energy, understanding this concept is critical. For instance, during activities like cycling, the body transforms chemical energy from food into kinetic energy for the movement and thermal energy as a form of heat. This heat is often considered 'waste', but it is simply a natural byproduct of the inefficiencies in energy conversion processes.

Consider a cyclist pedaling; their muscles are doing work, thereby manifesting mechanical energy. However, this process is not just about the production of mechanical energy. Due to the law of conservation of energy, which states that energy cannot be created or destroyed but only changed from one form to another, the energy that is not converted into mechanical work must reappear in some other form, which in this case, is heat. When a student encounters a problem like the one from our textbook, recognizing that the unaccounted-for energy is not missing but has transformed into heat is a key step towards finding the solution.
Mechanical Power
Mechanical power in physics describes the rate at which work is performed or energy is transferred in a mechanical system. It is essentially a measure of how quickly work can be done. For example, when a student looks at the mechanical power produced by the human body during cycling, it's crucial to realize that this figure (\(120 W\) in our exercise) represents the rate at which the cyclist performs mechanical work against the resistance of the pedaling and other forces such as friction and air resistance.

Understanding mechanical power can provide insights into the performance and capabilities of various systems. For instance, the provided exercise improvement advice suggests contemplating the individual effort and the mechanical output to appreciate the body's output power. The term 'watt' (\(W\)) is a unit of power named after James Watt, and it quantifies the energy conversion rate – one watt is equivalent to one joule of energy transferred or work done per second.
Efficiency of the Human Body
When students study the efficiency of the human body, they learn about the ratio of useful output to total input. Considering our exercise, the body's efficiency can be illustrated by comparing the mechanical power output during cycling (\(120 W\)) with the energy release rate from food consumption (\(500 W\)). The human body is not a perfect machine; a significant proportion of energy is lost, primarily as heat, due to various biochemical and mechanical inefficiencies.

In terms of improving one's grasp on this concept, it's helpful to analyze daily activities like walking, running, or cycling and estimate the energy consumed versus the useful work done. For the exercise in question, the body has an efficiency of \(120 W / 500 W = 0.24\), or 24%, when only mechanical work is considered. This implies that 76% of the energy input is not doing mechanical work; instead, it's dissipated as heat, which the exercise calculated as \(380 W\). This efficiency is a reminder of the marvel of human biology, as well as its limitations when it comes to energy conversion.

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Most popular questions from this chapter

A balloon contains 0.30 mol of helium. It rises, while maintaining a constant \(300-\mathrm{K}\) temperature, to an altitude where its volume has expanded five times. Neglecting tension forces in the balloon, how much work is done by the helium during this isothermal expansion?

A \(25-\mathrm{L}\) sample of ideal gas with \(\gamma=1.67\) is at \(250 \mathrm{K}\) and \(50 \mathrm{kPa} .\) The gas is compressed adiabatically until its pressure triples, then cooled at constant volume back to \(250 \mathrm{K},\) and finally allowed to expand isothermally to its original state. (a) How much work is done on the gas? (b) What is the gas's minimum volume? (c) Sketch this cyclic process in a \(p V\) diagram.

Does the first law of thermodynamics apply to irreversible processes?

The adiabatic lapse rate is the rate at which air cools as it rises and expands adiabatically in the atmosphere (see Application: Smog Alert, on page 302 ). Express \(d T\) in terms of \(d p\) for an adiabatic process, and use the hydrostatic equation (Equation 15.2 ) to express \(d p\) in terms of \(d y .\) Then, calculate the lapse rate \(d T / d y .\) Take air's average molecular weight to be 29 u and \(\gamma=1.4,\) and remember that the altitude \(y\) is the negative of the depth \(h\) in Equation 15.2.

Volvo's B5340 engine, used in the V70 series cars, has compression ratio \(10.2,\) and the fuel-air mixture undergoes adiabatic compression with \(\gamma=1.4 .\) If air at \(320 \mathrm{K}\) and atmospheric pressure fills an engine cylinder at its maximum volume, what will be (a) the temperature and (b) the pressure at the point of maximum compression?

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