Reconsider the resistor in the AC circuit from Question 12. The resistor is embe
ID: 1515063 • Letter: R
Question
Reconsider the resistor in the AC circuit from Question 12. The resistor is embedded in a cylindrical housing, which is filled with mineral oil. (Housing dimensions: length = 5.0 cm, diameter = 1.50 cm) Mineral oil has a specific heat of 1670 J/kg. K and a density of 850 kg/m^3. The ambient room temperature is 295 K. If the housing were made of a perfect insulator, how long will it take to heat the oil to 20 K above room temperature? If the housing were made of fiberglass with a wall thickness of 1.00 cm, how far above room temperature will the oil actually get before the power delivered by the resistor is equal to the rate at which heat is conducted out of the housing? The thermal conductivity of fiberglass is 0.04 W/m middot K.Explanation / Answer
(B) heat conducted outside by conduction=KA(delta T/delta x)
where delta T=temperature difference =T1=T-295 where T is temperature after increase
delta x is thickness=0.01 m
power supplied by resistor=0.16675 ( I have taken this value from the first part you solved)
area of house=2rh+2r^2=2.71*10^(-3) m^2
0.16675=0.04*2.71*10^(-3) *T1/0.01
we get T1=15.38 =answer
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