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
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
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)
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
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
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