A.) A hollow spherical iron container whose outer diameter is 70 cm and thicknes

Question

A.) A hollow spherical iron container whose outer diameter is 70 cm and thickness is 4 mm is filled with iced water at 0ºC. If the outer surface temperature is 3ºC, determine the approximate rate of heat loss from the sphere in watts.

B.)An escalator in a shopping center is designed to move 42 people, 66 kg each, at a constant speed of 0.5
m/s at 45° slope. Determine the minimum power input needed to drive this escalator. Answer in kW.

Any help with unit conversions would be greatly appreciated!

Explanation / Answer

rate of heat flow is Q/t = -K×A×T/x, where Q/t is the rate of heat flow; -K is the thermal conductivity factor; A is the surface area; T is the change in temperature and x is the thickness of the material (T/x is called the temperature gradient and is always negative

Q/t = -K×A×T/x,

Now putting all the vaues given

Q/t = -79.5*4*3.14*(.35^2)*3/(4*10^-3) ( K for iron is 79.5 W/mK )

= 91739 watt Or 91.7kW

Power = F*V = Mgsin(45) * .5 ( in cae of min power F = component of mg along inclined plane == Mgsin(45))

Power = 42*66*9.8*0.5/1.41 = 9633watt Or 9.63 kW

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