Ice starts forming in lake with water at `0^(@)C` and when the atmospheric temperature is `-10^(@)C`. If the time taken for `1 cm` of ice be `7` hours. Find the time taken for the thickness of ice to change from `1 cm` to `2 cm`

Options

A. 3.5hour
B. 7 hour
C. 14 hour
D. 21 hour

Answer

D

Explanation

As we have `t=(rho L)/(2k theta)y^(2)`
`rArr``(7 xx 3600) =((0.91)(80))/(2k(10))(1)^(2)`
`rArr` `k=(72.8)/(504000)`
`=1.44 xx 10^(-4) cal cm^(-1)``""^(@)C^(-1)`
To change from 1cm to 2cm thickness,
`t=(rho L)/(k theta) int_(1)^(2) ydy`
`rArr``t=(0.91 xx 80)/(2 xx 1.44 xx 10^(-4) xx 10)[2^(2)-1^(2)]`
`rArr`` t=(72.8)/(2.88 xx 10^(-3))(3)`
`rArr``t=(218.4)/(2.88 xx 10^(-3)) = 75.8 xx 10^(3) s`
`rArr``t= 21.06 h ~~ 21 hour `