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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 $4$ minutes 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 $= 336 \times 10^{3} J / k g$ and specific heat of water $= 4200 J / k g - K$ )

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$θ = 35 ° C$

$θ = 40 ° C$

$θ = 45 ° C$

$θ = 30 ° C$

answer is B.

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Detailed Solution

Let heat is supplied at a constant rate of $(α) \frac{J}{m i n}$ . In $4$ minutes, (when temperature remains constant) ice will be melting.

$∴ m L = (4) α$

$∴ \frac{α}{m} = \frac{L}{4} = \frac{336 \times 10^{3}}{4}$

$= 84 \times 10^{3} J / m i n - k g$

Now in last two minutes,

$Q = m s Δ θ$

$∴ (α) (2) = (m) (4200) (θ - 0 ° C)$

$Substituting the value of \frac{α}{m} we get,$

$θ = 40 ° C$

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