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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 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

A

`-10^(@)C`

B

`-20^(@)C`

C

`-30^(@)C`

D

`-40^(@)C`

Text Solution

Verified by Experts

The correct Answer is:
D
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`
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Knowledge Check

  • 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 . Final temperature at the end of 7 min is

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