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An iron bar of uniform cross-section and...

An iron bar of uniform cross-section and length one metre is kept with its one end in contact with ice at `0°C` and the other end in contact with water at `100°C`. The temperature at a certain point of the bar is `150°C` so that during the steady state, the quantity of ice melting is equal to that of steam produced in the same interval of time. Find the distance of the point ? [See Fig. 11.17]

Text Solution

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Let the distance of the point C be x from the cold end B (ice). The point C is maintained at 150°C. Let m be the mass of ice melted per second and .m. the mass of water at 100°C converted into steam per second. Given `AB= 1 m = 100` cm.
`m L_i (KA (150-0))/( x) " "...(i)`
where `L_i` is the latent heat of fusion of ice. If `L_s` is the latent heat of vaporisation of steam then,
`m L_s = (KA (150 - 100) )/( 100- x) " "...(ii)`
Dividing equation (i) by (ii)
`(L_i)/( L_s) = (150)/( 50) xx ((100 -x ))/( x)`
`L_i = 80` cal/gm `L_s = 540` cal/gm
`(80)/(540) = (3 (100-x) )/( x)`
`(0.148)/( 3) = (100-x)/(x) , 0.049 x = 100- x`
`x= 95.3` cm `= 0.953` m
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