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)`)

Options

A. `0.12 xx 10^(-5)`K
B. `1.9 xx 10^(-3)`K
C. `1.3 xx 10^(-4^(@))`C
D. `1.2 xx 10^(-3)`K

Answer

D

Explanation

d) Rate of production of mass of steam = `(dm)/(dt) = 1/(60) gs^(-1)`
Rate of heat transformed by stove,
`(dtheta)/(dt) = L(dm)/(dt)=540 xx 1/(60) = 9cal^(@)C^(-1)s^(-1)cm^(-1)`
Also, `(d(theta))/(dt) = (KAd(theta))/(dx)rArr L(dm)/(dt)=(KAd(theta))/dx`
`rArr 9 = (0.5 xx 3000xx d(theta))/(0.2)`
`rArr d(theta) = 1.2 xx 10^(-3^(@))C=1.2xx10^(-3)`K