A certain amount of ice is supplied heat at a constant rate for 7 min. For the first one minute the temperature rises uniformly with time. Then it remains constant for the next 4 min and again the temperature rises at uniform rate for the last 2 min. Given `S_("ice")=0.5cal//g^(@)C,L_(f)=80cal//g`.
The initial temperature of ice is

Options

A. `-10^(@)C`
B. `-20^(@)C`
C. `-30^(@)C`
D. `-40^(@)C`

Answer

D

Explanation

Let heat is supplied at a rate of `k_(1)"cal"//"min"` then
`k_(1) xx 1 = m(0.5)theta_(1)`
`k_(1)xx4 = m(80)` `" "` `k_(1) xx 2 = m(1)(theta_(2))`
`implies k_(1) = 20 m implies theta_(1) = 40^(@)C , theta_(2) = 40^(@)C`
Therefore initial temperature =`-40^(@)C`
Final temperature = `+40^(@)C`