Question

A steam pipe is covered with 1.50-cm thick insulating material of thermal conductivity of 0.200 cal/cm · °C · s. How much energy is lost every second when the steam is at 195°C and the surrounding air is at 20.0°C? The pipe has a circumference of 800 cm and a length of 40.0 m. Neglect losses through the ends of the pipe.

Answer 1

This question involves the concepts of Fourier's law of heat conduction and heat loss per unit time.

The heat energy loss per second is "3.12 x 10⁸ W".

Applying Fourier's Law of Heat Conduction here, we get:

$Q = -kA\frac{\Delta T}{\Delta x}$

where,

Q = heat energy loss per unit time = ?

k = thermal conductivity = 0.2 cal/cm.°C.s $(\frac{4.184\ J}{1\ cal})(\frac{100\ cm}{1\ m})$ =  83.68 J/m.°C.s

A = Surface area = (circumference)(length) = (8 m)(40 m) = 320 m²

ΔT = difference in temperature = 20°C - 195°C = -175°C

Δx =thickness of insulation = 1.5 cm = 0.015 m

Therefore,

$Q = -(83.68\ J/m.^oC.s)(320\ m^2)(\frac{-175\ ^oC}{0.015\ m})$

Q = 3.12 x 10⁸ W = 312 MW

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