Question

a steam pipe 20cm in diameter contains steam at 150'c and is covered with asbestos 5cm thick.the outside temp is kept at 60'c.by how much the thickness of the covering be increased in order that the rate of heat loss should be decreased by 25%?

Answer 1

Step-by-step explanation:

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Answer 2

Answer:

The thickness of the covering be increased in order that the rate of heat loss should be decreased by 25% will be 7.5cm

Step-by-step explanation:

Let heat flowing out through the surface be Q c/s

Let the radius of the pipe be X cm and the length 10 meter

Area of lateral Surface = $2\pi x$   Therefore,

   Q =  -k 2$\pix$$\pi x$

⇒ dt = $\frac{-q}{2\pi x} \frac{dx}{x}$    

           by  Integrating

⇒T = - q (Logx + c) ÷ 2πk

• Now T = 150, x = 10

         =   150 = -q(log10+c) ÷2πk  --------------------(i)

• Again when T=40, X= 15

         = 40 = -q (log10+c) ÷2πk   ---------------------(ii)

• Subtracting (ii) from (i), we get

        =   110 = -q (log2/5) ÷ 2πk  --------------------(iii)

• Let T= t, when x=12.5

         =   f   = -q (log12.5 + c) ÷2πk ------------------(iv)

• Subtracting (iv) from (i), we get

           = f - 150 = -q (log1.25) ÷ 2πk ----------------(v)

• Dividing (v)  by (iii) we get,

                   T = 89.5°

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