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A boiler is made of a copper plate 3 mm ...

A boiler is made of a copper plate 3 mm thick. The inner surface of the copper plate is coated with a layer of tin of thickness 0.3 mm. The surface of the plate exposed to the gas at 700°C is `150 "cm"^2`.Find the maximum amount of steam that could be produced per hour at atmospheric pressure. The coefficient of thermal conductivities of copper and tin are 397 Wm`""^(-1) "K"^(-1) and 63 "Wm"^(-1) "K"^(-1)`.

Text Solution

Verified by Experts

`theta_1 = 700^(@) C " " theta_2 = 100^(@) C`
Let the temperature of the interface be `theta` (see Fig. 11.5). During the steady state the rate of heat flow through copper is equal to the rate of heat flow through tin.
Thermal conductivity of copper `= k_1 = 397 "Wm"^(-1) "K"^(-1)`
Thermal conductivity of tin `= k_2 = 63 "Wm"^(-1) "K"^(-1)`
`(Q)/( t) = (k A ( theta_1 - theta_2))/( x) `
`((Q)/( t))_("for copper")= ((Q)/( t))_("for tin")`
`(397 xx A (700-theta))/( 3 xx 10^(-3) ) = (63 xx A ( theta - 100))/( 0.3 xx 10^(-3) )`
`700- theta = (630)/( 397) ( theta - 100) = 1.59 ( theta - 100)`
`1.59 theta + theta = 700+ 159 = 859`
`theta = (859)/( 2.59) = 331.7K`
Heat flowing through copper per hour
`= (KA ( theta_1 - theta) )/( x )t`
`= ( 397 xx 150 xx 10^(-4) xx ( 700 - 331.7) xx 60 xx 60)/( 3 xx 10^(-3) )`
`= 2.63 xx 10^(10)` J
Latent of steam `= L = 2268 xx 10^(3) J//kg`
Mass of steam produced in one hour
`= m = (2.63 xx 10^(10) )/( 2268 xx 10^3) = 1.16 xx 10^4` kg
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