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? .

A steam cylindrical pipe of radius 5 cm carries steam at `100^@C` . Th

1.	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? .
Answer» Correct Answer - 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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