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Calorimetry

Question

The melting temperature of a certain mass of a solid object is 20°C. When a heat Q is added to the object, its $\frac{3}{4}$ material melts. When an additional amount of Q heat is added the material transforms to its liquid state at 50°C. Find the ratio of specific latent heat of fusion (in J/g) to the specific heat capacity of the liquid (in J g^-1 °C^-1) for the material.

Moderate

Solution

Let the mass of the solid object be m, and specific latent heat of fusion be L ,
According to problem, $Q = \frac{3}{4} mL$ ……..(i)
$2 Q = mL + ms (50 - 20)$ ………(ii)
From (i) and (ii), $\frac{3}{2} mL = mL + 30 ms$
$\Rightarrow \frac{L}{2} = 30 s \Rightarrow \frac{L}{s} = 60$

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