Water is boiled in flat bottom kettle placed on a stove. The area of the bottom is 3000 `"cm"^(2)` and the thickness is 2 mm. If the amount of steam produced is 1 g `"min"^(-1)` , the difference of temperature between the inner and outer surfaces of the bottom is (Given : Thermal conductivity of the material of kettle is 0.5 cal `""^@C^(-1) s^(-1) "cm"^(-1)` and latest heat of steam is 540 cal `g^(-1)`)

Options

A. `2.1xx10^(-3)""^@C`
B. `3.1xx10^(-3) ""^@C`
C. `1.2xx10^(-3) ""^@C`
D. `2.5xx10^(-3) ""^@C`

Answer

C

Explanation

Mass of steam produced per second ,
`(dm)/(dt) = 1/60 g s^(-1)`
Heat transferred per second , `(dQ)/(dt)=L (dm)/(dt)`
`rArr (dQ)/(dt)=540xx1/60 "cal s"^(-1)`
Also `(dQ)/(dt)=(KA DeltaT)/d`
`therefore DeltaT=(dQ)/(dt)xxd/(KA)=(9xx0.2)/(0.5xx3000)=1.2xx10^(-3) ""^@C`