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Latent Heat of Vaporisation

1 g ice of ...

Question

$1 g$ ice of $0^{\circ} C$ and $1 g$ vapour at $100^{\circ} C$ are mixed together. Assuming no heat loss, what will be the final temperature of the mixture?

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Solution

Let final temperature be T
Heat lost by vapour $=$ Heat gained by ice
$m l_{v} + m s (100 - T) = m l_{f} + m s (T - 0) 1.530 c a l / g + 1.1 c a l / g ° C \times (100 - T) = 1.80 c a l / g + 1.1 c a l / g ° C \times T \Rightarrow 530 + 100 - T = 80 + T \Rightarrow 550 = 2 T T = 275 ° C$
$∵$ T cannot be greater than $100 ° C$
$t h e r e f o r T = 100 ° C$

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