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# The specific latent heat of fusion of water is:(A) $80{\text{ cal }}{{\text{g}}^{{\text{ - 1}}}}$ (B) $2260{\text{ J }}{{\text{g}}^{{\text{ - 1}}}}$ (C) $80{\text{ J }}{{\text{g}}^{{\text{ - 1}}}}$ (D) $3366{\text{ cal }}{{\text{g}}^{{\text{ - 1}}}}$

Last updated date: 13th Jun 2024
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Hint: The specific latent heat of fusion of water is 334 Joules per gram. Convert it into calories per gram using the conversion 1 calorie = 4.184 Joules or 1 Joule = 0.239 calories.

Complete step by step solution
We know that the change of state from solid to liquid (or ice to water here) is termed as fusion. When a solid is heated, its temperature increases till it reaches the melting point of the solid, then for a while, the increase in temperature on applying heat stops. This is because the substance starts changing its state from solid to liquid, i.e. the solid substance starts melting. During change of state from one state to another, the temperature remains constant. In our case, when heat energy is added to ice at its melting point, i.e. at 0°C, it changes into the same mass of water at 0°C.
This happens because the heat applied at that time is used up in changing the state of the substance rather than in increasing the temperature of the substance. This heat energy, required to change the state of a substance is called latent heat. There are basically two types of latent heats, one for fusion and one for vaporization. In our question, we require the latent heat of fusion.
We know that the Latent heat of fusion of water is 334 Joules per gram or 334000 Joules per Kilogram. We will convert this into calories per gram to match an answer from the options.
$\because 1J = 0.239cal \\ \Rightarrow 1J/g = 0.239cal/g \\ \Rightarrow 334J/g = 334 \times 0.239cal/g \\ \Rightarrow 334J/g = 79.826cal/g \\ \Rightarrow 334J/g \approx 80cal/g \\$

Therefore, option (A): 80 cal g-1 is correct.

Note: Here, one should be careful not to confuse latent heat of fusion and specific latent heat of fusion. Latent heat of fusion is the amount of energy required to change the state of a given mass of substance from solid to liquid whereas the specific heat of fusion is the amount of energy required to change the state of a 1kg of substance from solid to liquid.
The relation between the two is ${L_f} = \dfrac{{{Q_f}}}{M}$.
where, $L_f$ is the specific latent heat of fusion of the substance
$Q_f$ is the latent heat of fusion of the substance
and M is the mass of the substance