If the Universe is closed, then its age will be
a. less than two-thirds of 1/H.
b. more than two-thirds of 1/H.
c. equal to 1/H.
d. equal to H squared.
e. equal to the square-root of H.
a
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Suppose that a pipe carrying a hot fluid with an external temperature of Ti and outer radius ri is to be insulated with an insulation material of thermal conductivity k and outer radius ro. Show that if the convective heat transfer coefficient on the outside of the insulation is h and the environmental temperature is T?, the addition of insulation can actually increases the rate of heat loss if ro < k /h and that maximum heat loss occurs when ro = k/h . This radius, rc, is often called the critical radius.
GIVEN
An insulated pipe External temperature of the pipe = Ti Outer radius of the pipe = ri Outer radius of insulation = ro Thermal conductivity = k Ambient temperature = T? Convective heat transfer coefficient = h
FIND
Show that (a) The insulation can increase the heat loss if ro < k/h (b) Maximum heat loss occurs when ro = k/h
ASSUMPTIONS
The system has reached steady state The thermal conductivity does not vary appreciably with temperature Conduction occurs in the radial direction only
SKETCH
Is it possible to see a waxing crescent moon on the overhead meridian at 10 A.M. local time? How about at 4 P.M. local time? Explain your answers
Calculate the displacement amplitude (in m) of a 20 kHz sound wave in helium if it has a pressure amplitude of 8.0 × 10^-3 N/m2 . (r = 0.179 kg/m3, v = 972 m/s.)
a. 2.9 × 10^-10 b. 3.7 × 10^-10 c. 7.8 × 10^-9 d. 2.4 × 10^-9 e. 1.9 × 10^-10
The fundamental force that governs the motion of the planets is
A. strong force. B. weak force. C. electromagnetic force. D. gravitational force.