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Thermal Equilibrium

A hot liquid ...

Question

A hot liquid having mass 100g in a container is constantly losing heat at the rate of 3 K/min. Just after it begins to solidify, the temperature of system remains constant for about 30 min. Find the latent heat of liquid.

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Solution

Consider man of liquid be $M$ and latent near capacity $L$ .
It in loosing reat at a rate $= 3 k / m i n = 0.05 k / s$
as, $Q = M L$ , we get, $\frac{d Q}{d t} = \frac{M L}{t} = 0.05 k / s$
temp, remains constant for $30 m i n$ , so,
Latent Heat consumed $= 0.05 \times 30 \times 60 = 90$
as $M L = 90$ , where $M = 0.1 k g$
$\Rightarrow L = \frac{90}{0.1} = 900 J / k g$

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