Water is being boiled in flat bottom kettle placed on a stove. The area of the bottom is `3000cm^2` and the thickness is 2 mm. If the amount of steam produced is `1g//min`, calculate the difference of temperature between the inner and outer surface of the bottom. K for the material of kettle is 0.5`cal^@C//s//cm`, and the latent heat of steam is `540 cal//g`.

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