Problem 3.1 A small spherical bead of mass m is preheated to a temperature of 1,100 K (state 1) and immediately thrown into a pool of water at room temperature. At state 2, the following relation is obtained from conservation of the energy: 1₂ U₂ −U¸ + − m $504, (T,'`(1) – Tam) dt (v² − v² ) + mg (z₂ − z₁ ) = [hconv4s (T₂(t) – Twater) dt + (v√32-1 A¸ surr 4 Change in kinetic energy Heat loss to the liquid due to convection Heat loss to the surroundings due to radiation Knowing that t is time, T is temperature, g is the gravitational constant, A is the surface area of the bead, o is the Stefan-Boltzmann constant o = 5.67 × 10-8 W/(m². K4) and that the equation is dimensionally consistent, (a) Show that the kinetic and potential energy terms have the same base units. Change in internal energy Change in potential energy Determine the dimensions (combination of [Mass], [Length], [Time] and [Temperature]) and units (in base SI, e.g., combination of [kg], [m], [s] and [K]) of the following terms: (b) Internal energy, U (c) Convective heat transfer coefficient, hconv (d) Emissivity, &. Show all your work for full credit.

Problem 3.1 A small spherical bead of mass m is preheated to a temperature of 1,100 K (state 1) and immediately thrown into a pool of water at room temperature. At state 2, the following relation is obtained from conservation of the energy: 1₂ U₂ −U¸ + − m $504, (T,'`(1) – Tam) dt (v² − v² ) + mg (z₂ − z₁ ) = [hconv4s (T₂(t) – Twater) dt + (v√32-1 A¸ surr 4 Change in kinetic energy Heat loss to the liquid due to convection Heat loss to the surroundings due to radiation Knowing that t is time, T is temperature, g is the gravitational constant, A is the surface area of the bead, o is the Stefan-Boltzmann constant o = 5.67 × 10-8 W/(m². K4) and that the equation is dimensionally consistent, (a) Show that the kinetic and potential energy terms have the same base units. Change in internal energy Change in potential energy Determine the dimensions (combination of [Mass], [Length], [Time] and [Temperature]) and units (in base SI, e.g., combination of [kg], [m], [s] and [K]) of the following terms: (b) Internal energy, U (c) Convective heat transfer coefficient, hconv (d) Emissivity, &. Show all your work for full credit.

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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Question

Problem 3.1
A small spherical bead of mass m is preheated to a temperature of 1,100 K (state 1) and
immediately thrown into a pool of water at room temperature. At state 2, the following relation
is obtained from conservation of the energy:
1₂
U₂ −U¸ + − m $504, (T,'`(1) – Tam) dt
(v² − v² ) + mg (z₂ − z₁ ) = [hconv4s (T₂(t) – Twater) dt +
(v√32-1
A¸
surr
4
Change in
kinetic energy
Heat loss to the liquid due to convection Heat loss to the surroundings due to radiation
Knowing that t is time, T is temperature, g is the gravitational constant, A is the surface area of
the bead, o is the Stefan-Boltzmann constant o = 5.67 × 10-8 W/(m². K4) and that the
equation is dimensionally consistent,
(a) Show that the kinetic and potential energy terms have the same base units.
Change in
internal energy
Change in
potential energy
Determine the dimensions (combination of [Mass], [Length], [Time] and [Temperature]) and
units (in base SI, e.g., combination of [kg], [m], [s] and [K]) of the following terms:
(b) Internal energy, U
(c) Convective heat transfer coefficient, hconv
(d) Emissivity, &.
Show all your work for full credit.

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