15 - Heat Transfer Questions Answers

A bullet of mass 1 gm moving with a speed of 20m/s hits an ice block of mass 990 gm kept on a frictionless floor and gets tuck in it. the amount of ice that melts, if 50% of the lost kinetic energy goes to ice will be

(1) 0.030 g

(2) 0.30 g

(3) 0.0003 g

(4) 3.0 g

Asked By: HIMANSHU MITTAL
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Joshi sir comment

amount of energy given by bullet = 0.5 (1/2) m v2 / 4.2 cal.

and amount of energy received by the ice block = ML   here L is latent heat and M is mass of ice melted

on comparing we will get  m v2/(4*4.2) = M*80 or M = 1*400/16.8*80 = 5/16.8 = 0.30 gm 

a metallic sphere having inner radius a and outer radius b has thermal conductivity k = ko(k not)/r² (a ≤ r ≤ b). the thermal resistance between inner and outer surface for radiant heat flow is 

Asked By: HIMANSHU MITTAL
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Joshi sir comment

consider a sphere of radius r and thickness dr 

formula used is H = KAdT/L so dT/H = L/KA or R = L/KA,  dT/H is thermal resistance

thermal resistance of layer of thickness dr is dr/K4πr2, on putting the value of K we get

 dR = r2dr/4πr2k0

or dR = dr/4πk0

now integrate within the proper limits

Assuming the sun to be aspherical body of radius R at a temperature of T K, evaluate the total radiant power incident on earth, at a distance r from the sun. Take radius of earth as Ro(R not)

Asked By: HIMANSHU MITTAL
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Joshi sir comment

Total radiant power given by the sun = σAT4 = 4πR2σT4

amount received on the surface of earth = (πR02/4πr2)*4πR2σT4

A body emits radiant energy 1600Js‾¹ when it is at temperature 273 °C. if its temperature decreases to 273 K them it emits radiant energy at the rate of

(1) 0

(2) 800 Js‾¹

(3) 400 Js‾¹

(4) 100 Js‾¹

Asked By: HIMANSHU MITTAL
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Joshi sir comment

Temprature of second case is half of the temprature of first case so according to stefan's law radiant power will become 1/16 part = 100

A thermally insulated piece of metal is heated by supplying a constant power P. Due to this, the temperature of the metal starts varying with time as T= at^1/4 + To(T not)

The heat capacity of the metal as a function of temperature is

(1) 4PT³/a^4

(2) 4P(T-To)³/a^4

(3) 4PT²/a³

(4) 4P(T - To)²/a³

Asked By: HIMANSHU MITTAL
is this question helpfull: 4 2 submit your answer
Joshi sir comment

P = dQ/dt = mcdT/dt

or mcdT = Pdt

or mc = Pdt/dT

or mc = Pd/dT[(T-T0)4/a4]

here mc is heat capacity

now solve 

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