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Chapter 9: Problem 16

The ABC Evening News Report in a news segment on hypothermia research sudies af the University of Minnesota claimed that heat loss from the body is 30 fimes faster in \(10^{\circ} \mathrm{C}\) watter than in air at the samme temperature. Is that a realistic statement?

Short Answer

Expert verified
Yes, it's realistic since water conducts heat more effectively than air.

Step by step solution

01

Understand the Concept of Heat Loss

Heat loss from the body into the environment can be influenced by various factors, such as the medium (air or water), temperature difference, and surface area exposed. Water, being a better conductor than air, accelerates heat loss.
02

Analyze Heat Conduction in Air and Water

The heat transfer in water is significantly higher as water has a thermal conductivity about 24 times greater than air. This means water can remove heat from the body faster than air at the same temperature.
03

Consider the Assertion in Context

The claim is that the rate of heat loss is 30 times faster in water than in air at the same temperature. Since water conducts heat better and causes more convective heat loss, it is plausible for the rate to be significantly higher, potentially close to the stated figure.
04

Conclude on Realistic Expectation

While the exact factor of 30 may vary depending on individual conditions such as body fat, motion, and clothing, the claim aligns with the understanding that significant differences in heat loss exist between water and air.

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Key Concepts

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

Conduction
Conduction is a key concept in understanding how heat is transferred from one material to another. In the context of the exercise, we compare heat transfers between air and water at the same temperature. When we talk about conduction, we are looking at how heat moves through materials. It happens at the molecular level. Molecules vibrating due to heat bump into each other, passing the energy along.
- In the human body, heat from blood vessels is transferred to surrounding tissues through conduction.
- This process is more efficient in water than in air because water molecules are closer together, making it easier for vibrations to be passed along.
Conduction is crucial to understanding why heat is lost more rapidly in water. Water's higher density allows it to conduct heat away from a source much more effectively than air.
Thermal Conductivity
Thermal conductivity refers to a material's ability to conduct heat. In our exercise, thermal conductivity is what makes water significantly better at drawing heat from the body compared to air. - Thermal conductivity is measured in Watts per meter per degree Kelvin (W/m/K), and water's notably higher figure compared to air indicates that it can transfer heat more effectively.
- Water's thermal conductivity is about 24 times greater than that of air, which aligns with the exercises鈥� claim that heat loss is substantially increased in water.
This property highlights a significant reason humans lose body heat more quickly in water. Understanding thermal conductivity helps make sense of why water environments feel so much colder than air of the same temperature.
Convective Heat Loss
Convective heat loss is another important aspect of how bodies lose heat. Convection involves the movement of fluid molecules (liquid or gas) around the body, helping transfer heat away.
- In water, convection plays a significant role because movement increases the circulation of water around the body, stripping heat away even faster.
- When we move in the water, new layers of cold water continuously replace the warmer water closest to our skin, accelerating heat loss.
This explains why staying still in cold water can feel less chilling than swimming. Overall, convective heat loss combines with conduction and thermal conductivity to explain why water at the same temperature as air makes you feel colder.

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Most popular questions from this chapter

A horizontal uninsulated steam pipe passes through a large rocm whose walls and ambient air are at \(300 \mathrm{~K}\). The pipe of \(150-\mathrm{mm}\) diameter has an emissivity of \(0.85\) and an couter surface temperature of \(400 \mathrm{~K}\). Calculate the heat loss per unit length from the pipe.

A circular grill of diameter \(0.25 \mathrm{~m}\) and emissivity \(0.9\) is maintained at a constant surface temperature of \(130^{\circ} \mathrm{C}\). What electrical power is required when the room air and surroundings are at \(24^{\circ} \mathrm{C}\) ?

Consider two long vertical plates maintaincd at unifomm temperatures \(T_{a, 1}>T_{a, 2}\). The plates are open at their ends and are separated by the distance \(2 l\). (a) Sketch the velocity distribution in the space between the plates. (b) Write appropriate forms of the continuity, momentum, and energy cquations for laminar fow between the plates. (c) Evaluate the temperature distribution, and express your result in terms of the mean temperature, \(T_{m}=\) \(\left(T_{n 1}+T_{s .2}\right) / 2\).

A vertical array of circuit boards is immersed in quiescent ambient air at \(T_{z}=17^{\circ} \mathrm{C}\). Although the components protrude from their substrates, it is reasonable, as a first approximation, to assume flat plates with uniform surface heat flux \(q_{x}^{\prime \prime}\). Consider boards of length and width \(L=W=0.4 \mathrm{~m}\) and spacing \(S=25 \mathrm{~mm}\). If the maximum allowable board temperature is \(77^{\circ} \mathrm{C}\), what is the maximum allowable power dissipation per board?

Water at \(35^{\circ} \mathrm{C}\) with a velocity of \(0.05 \mathrm{~m} / \mathrm{s}\) flows over s horizontal, 50 -mm-diameter cylinder maintained at a uniform surface temperature of \(20^{\circ} \mathrm{C}\). Do you anticipate that heat transfer by free convection will be significant? What would be the situation if the fluid were air \(z\) atmospheric pressure?
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