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A steam cylindrical pipe of radius 5 cm ...

A steam cylindrical pipe of radius 5 cm carries steam at `100^@C` . The pipe is covered by a jacket of insulating material 2 cm thick having a thermal conductivity 0.07 `W//m-K` . If the temperature at the outer wall of the pipe jacket is `20^@C` , how much heat is lost through the jacket per metre length in an hours?
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Text Solution

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The correct Answer is:
A, C
Thermal resistance per metre length of an element at distance r of thickness dr is
`dR = (dr)/(K(2pir))" " (R = l/(Ka))`
`:.` Total resistance `R = int _(r_1= 5cm)^(r_2 = 7cm) dR`
`=1/(2piK) int_(7.0 xx 10^-2 m)^(5.0 xx 10^-2 m) (dr)/r`
`= 1/(2piK) In (7/5)`
`=1/((2pi)(0.07)) In (1.4)`
= 0.765 `K//W`
Heat current , `H = ("Temperature difference")/("thermal resistance")`
`(100 -20)/(0.765) = 104.6W`
`:." Heat lost in one hour" = "Heat current" xx "time"`
`= (104.6)(3600)J`
`= 3.76 xx (10^5)J`.
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