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Water is being boiled in a flat bottomed...

Water is being boiled in a flat bottomed kettle placed on a stove . The area of the bottom is `300 cm^(2)` and the thickness is 2 mm. If the amount of steam produced is 1 g `min^(-1)`, then the difference of the temperature between the inner and outer surfaces of the bottom is (thermal conductivity of the material of the lettle =`0.5 cal cm^(-1)^(@)C s^(-1)` and latent heat of the steam is equal to to `540 cal g^(-1)`)

Text Solution

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Mass of steam produced`=(dm)/(dt)=(1)/(60)g//s`
Heat transferred per second
`=(dH)/(dt)=L(dm)/(dt)implies(dH)/(dt)=540xx(1)/(60) cal//s=9 cal//s`
Area`=3000cm^2`, `K=0.5 cal^@C//s//cm`
`theta=` temperature difference
`d=` thickness = 2mm =0.2cm
`(dH)/(dt)=(KAtheta)/(d)impliesL(dm)/(dt)=(KAtheta)/(d)`
`implies9=(0.5xx3000xxtheta)/(0.2)impliestheta=1.2xx10^(-3@)C`
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