A steam pipe of radius `5cm` carries steam at `100^(@)C` The pipe is covered by a jacket of insulating material `2cm` thick having a ther mal conductivity `0.07Wm^(-1) k^(-1)` if the tempera ture at the outer wall of the pipe jacket is `20^(@)C` how much heat is lost through the jacket per mater lenght in an hour ? .

Explanation

`dR=(dr)/(K(2pir)) ( :' R=(1)/(KA))`
Total resistance `R =underset(r_(1))overset(r_(2))intdR =(1)/(2piK)underset(5xx10^(-2))overset(7xx10^(-2))int(dr)/(R )`
`= (1)/(2piK) In ((7)/(5)) = (1)/((2pi)(0.07))"in"(1.4) =0.765K//W`
Heat current `H = ("Temperature difference")/("Thermal resistance")`
`= ((100-20))/(0.765) =104.6W`
Heat lost in one hour = Heat current x time
`= (104.6)(3600) J =3.76 xx 10^(5)J`
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