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A certain amount of ice is supplied heat...

A certain amount of ice is supplied heat at a constant rate for 7 minutes. For the first one minute the temperature rises uniformly with time. Then, it remains constant for the next 4 minute and again the temperature rises at uniform rate for the last two minutes. Calculate the final temperature at the end of seven minutes.
(Given, L of ice `= 336 xx (10^3) J//kg` and specific heat of water `= 4200 J//kg-K`).

Text Solution

Verified by Experts

The correct Answer is:
C, D
Let heat is supplied at a constant rate of `(alpha) J/(min)`.
In 4 minutes, (when temperature remains constant)
ice will be melting.
`:. } mL = (4) alpha`
`:. alpha/m = L/4 = (336 xx (10^3))/4`
`=84 xx (10^3) J//min-kg`
Now in last two minutes,
`Q = msDeltatheta`
`:. (alpha)(2) = (m)(4200)(theta - 0^@C)`
Substituting the value of `alpha/m` we get,
`theta = 40^@C` .
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