Volumetric expansion coefficients of simple materials are often well cataloged. However, the thermal expansion coefficientB of a human body is less well known. This could affect the human body's specific gravity and, therefore, measurements ofits body-fat ratio.Suppose that a human body of weight wo on dry land is placed on a scale while completely immersed in formaldehyde oftemperature T1- Once the temperature increases by AT, the scale reading drops by Aw.Derive an expression for ß in terms of AT, wo, and Aw by assuming that the ratio of the density of formaldehyde ef and theinitial density of the body Po is R = Pf/pb. Assume also that pf does not change when heated.B =%3DIf the body weighs 237.2 lb on dry land and his weight reading lowers by 0.237 lb when the formaldehyde is heated from63.40 °F to 82.80 °F, calculate the coefficient of volume expansion of the body.* Assume R = 0.820.1/°CB =

The reading on the scale when the body is completely immersed in formaldehyde, N1=wo-Vρfg The new reading on the scale after an increase in temperature will be, N2=wo-V'ρfg Subtract the above equations, N1-N2=wo-Vρfg-wo-V'ρfgN1-N2=Vρfg-V'ρfg∆w=ρfgV-V'Also, we know that, ∆V=βV∆TSo,∆w=ρfg∆V∆w=ρfgβV∆T∆w=ρfρbρbgβV∆TBut,wo=ρbgV∆w=ρfρbwoβ∆TBut,R=ρfρb∆w=Rwoβ∆Tβ=∆wRwo∆TNow it is given that, wo=237.2 lb,∆w=0.237 lb,∆T=82.80 °F-63.40 °F∆T=19.4 °FR=0.82 Calculate the coefficient of volume expansion, β=∆wRwo∆Tβ=0.2370.82×237×19.4β=6.286×10-5 °F-1

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Mechanical Engineering

Derive an expression for ß in terms of AT, wo, and Aw by assuming that the ratio of the density of formaldehyde pf and the initial density of the body po is R = p¢lP. Assume also that pr does not change when heated.

Derive an expression for ß in terms of AT, wo, and Aw by assuming that the ratio of the density of formaldehyde pf and the initial density of the body po is R = p¢lP. Assume also that pr does not change when heated.

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Concept explainers

Atomic diffusion in solids

In material science, diffusion can take place in solid, liquid, and gases. In solids, atomic diffusion can take place with the help of thermally activated and randomly vibrating atoms. The atomic diffusion in solids is complex and very slow in comparison to atomic diffusion in liquids and gases because the interatomic distance between the atoms is smaller in solids as compared to liquids and gases.

Question

Volumetric expansion coefficients of simple materials are often well cataloged. However, the thermal expansion coefficient
B of a human body is less well known. This could affect the human body's specific gravity and, therefore, measurements of
its body-fat ratio.
Suppose that a human body of weight wo on dry land is placed on a scale while completely immersed in formaldehyde of
temperature T1- Once the temperature increases by AT, the scale reading drops by Aw.
Derive an expression for ß in terms of AT, wo, and Aw by assuming that the ratio of the density of formaldehyde ef and the
initial density of the body Po is R = Pf/pb. Assume also that pf does not change when heated.
B =
%3D
If the body weighs 237.2 lb on dry land and his weight reading lowers by 0.237 lb when the formaldehyde is heated from
63.40 °F to 82.80 °F, calculate the coefficient of volume expansion of the body.* Assume R = 0.820.
1/°C
B =

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