Question

a pipe 10cm in diameter contains steel at 100°c it is covered with asbestos 5cm thick with thermal conductivity k=0.0006 and the outside surface is at 30°c find amount of heat lost per hour from a meter long pipe

Answer 1

Amount of heat lost per hour is 137058.5707 cal

Answer 2

Answer:

The amount of heat lost per hour from a meter long pipe is 137058.57 calories.

Step-by-step explanation:

Given,

• Diameter of pipe = 10 cm
• Temperature of pipe = 100°C
• Thickness of asbestos = 5 cm
• Outside temperature = 30°C
• Thermal conductivity k = 0.0006

Formula:

$q = - k A \frac{dt}{dx}$     ..........................................(1)

A = area = 2 π x

q = -2 π x . k . $\frac{dt}{dx}$    ..............................(2)

q × $\frac{dx}{x}$ =  -2 π x dt

$\frac{q}{2 \pi k}$ ∫ $\frac{dx}{x}$  = - ∫ dt   ..................................(3)

Limits given are:

x = 5 → 10 and t = 100 → 30

Substitute the limits in equation (3) and integrate the equation. we get,

$\frac{q}{2 \pi k} log (\frac{10}{5} )$ = 100 - 30

$q = \frac{70 ( 2 \pi k )}{log 2 } cal/ sec$

$q = \frac{(70) (2 \pi ) ( 0.0006) }{ log 2}$

Now the required heat loss = q × 100 × 60 × 60

$Heat loss = \frac{ (70) (2\pi ) (0.0006)}{log 2} (100) (60) (60)$

Where 100 = length of the pipe 1 m

Heat loss = 137058.57 calories

Therefore, The amount of heat lost per hour from a meter long pipe is 137058.57 calories.

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