(b) A probe and an asteroid collide in space. A disc made of copper, of diameter 56 m and thickness 1.2 m at a temperature of 850°C, is dislodged from the probe and floats freely in space, rotating about its axis of symmetry with an angular speed w = 25 rad s-1. The disc radiates heat, and its temperature falls to 20°C. Assume that no external torque acts on the disc. Find: (i) the change in kinetic energy of the disc, given the disc radius shrinks by an amount Ar (aXouAT")r; for a temperature change AT, where r, is the initial radius and au = 1.67 × 10-5 °C-1; (ii) the change in internal energy of the disc; and (iii) the amount of energy radiated by the disc.
(b) A probe and an asteroid collide in space. A disc made of copper, of diameter 56 m and thickness 1.2 m at a temperature of 850°C, is dislodged from the probe and floats freely in space, rotating about its axis of symmetry with an angular speed w = 25 rad s-1. The disc radiates heat, and its temperature falls to 20°C. Assume that no external torque acts on the disc. Find: (i) the change in kinetic energy of the disc, given the disc radius shrinks by an amount Ar (aXouAT")r; for a temperature change AT, where r, is the initial radius and au = 1.67 × 10-5 °C-1; (ii) the change in internal energy of the disc; and (iii) the amount of energy radiated by the disc.
Principles of Heat Transfer (Activate Learning with these NEW titles from Engineering!)
8th Edition
ISBN:9781305387102
Author:Kreith, Frank; Manglik, Raj M.
Publisher:Kreith, Frank; Manglik, Raj M.
Chapter8: Natural Convection
Section: Chapter Questions
Problem 8.26P
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Question
![(b) A probe and an asteroid collide in space. A disc made of copper, of diameter 56 m
and thickness 1.2 m at a temperature of 850°C, is dislodged from the probe and floats
freely in space, rotating about its axis of symmetry with an angular speed w = 25 rad
s-1. The disc radiates heat, and its temperature falls to 20°C.
Assume that no external torque acts on the disc.
Find:
(i) the change in kinetic energy of the disc, given the disc radius shrinks by an
amount Ar = (acuAT}r; for a temperature change AT, where r; is the initial
radius and aeu = 1.67 × 10-5 °C-1;
(ii) the change in internal energy of the disc; and
(iii) the amount of energy radiated by the disc.
Note:
Moment of inertia of a disc of mass M and radius R, I = }M R?
Density of copper, Pou = 8960 kg m-3
Specific heat capacity of copper, Ccu = 385 J (kg °C)-1](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0afb125e-6b2c-4169-ab67-74545bf400c6%2Fe6f72586-45b3-4428-bf0e-325400a9675b%2Fmg37iht_processed.png&w=3840&q=75)
Transcribed Image Text:(b) A probe and an asteroid collide in space. A disc made of copper, of diameter 56 m
and thickness 1.2 m at a temperature of 850°C, is dislodged from the probe and floats
freely in space, rotating about its axis of symmetry with an angular speed w = 25 rad
s-1. The disc radiates heat, and its temperature falls to 20°C.
Assume that no external torque acts on the disc.
Find:
(i) the change in kinetic energy of the disc, given the disc radius shrinks by an
amount Ar = (acuAT}r; for a temperature change AT, where r; is the initial
radius and aeu = 1.67 × 10-5 °C-1;
(ii) the change in internal energy of the disc; and
(iii) the amount of energy radiated by the disc.
Note:
Moment of inertia of a disc of mass M and radius R, I = }M R?
Density of copper, Pou = 8960 kg m-3
Specific heat capacity of copper, Ccu = 385 J (kg °C)-1
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