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`).

Options

A. `20^@C`
B. `45^@C`
C. `40^@C`
D. `25^@C`

Answer

C

Explanation

In the first interval of 1 min ice is heated to its melting point from its initial temperature which is below the melting point. In the next 4 min there is phase change. In the next 2 minutes there is heating of water let Q be the rate of supply of heat in joule per minute
`4Q=mL`
`=mxx336xx10^3`
and `2Q=mxx4200xxtheta`
On dividing`(4Q)/(2Q)=(mxx336xx10^3)/(mxx4200xxtheta)`
`theta=(336xx10^3)/(2xx4200)=40^@C`