To calculate the heat required to melt a sample, you use the equation for latent heat of fusion. The latent heat of fusion refers to the amount of heat energy required to change a substance from a solid to a liquid state without a change in temperature. The equation is:
[ Q = m \times L_f ]
Where:
- ( Q ) is the heat required (in joules or calories),
- ( m ) is the mass of the substance (in grams or kilograms),
- ( L_f ) is the specific latent heat of fusion (in J/kg or cal/g).
Detailed Explanation:
-
Mass (( m )): This is the amount of the substance you are melting, measured in grams or kilograms. The choice between grams and kilograms depends on the units used for the latent heat of fusion.
-
Specific Latent Heat of Fusion (( L_f )): This is a property of the substance and represents the amount of heat required to change one unit of mass (1 kg or 1 g) from solid to liquid at its melting point. It does not depend on the mass of the substance but on the substance itself. From the provided references, the specific latent heat of fusion for the substance discussed is -79.7 cal/g or -330,000 J/kg. Note that the negative sign typically indicates heat release during freezing (opposite of melting), so for melting, this value should be positive.
-
Heat Required (( Q )): This is the result of the multiplication of the mass of the substance and its specific latent heat of fusion. It tells you how much heat energy is needed to melt the entire sample at its melting point.
Example Calculation:
If you have a sample of 500 grams of a substance with a specific latent heat of fusion of 79.7 cal/g, the heat required to melt this sample would be:
[ Q = 500 , \text{g} \times 79.7 , \text{cal/g} = 39,850 , \text{cal} ]
This calculation shows that 39,850 calories of heat are needed to melt a 500-gram sample of this substance at its melting point.
Correction and Review:
The references provided initially listed the latent heat values with negative signs, which typically indicate heat release during the reverse process (freezing). For the calculation of heat required during melting, these values should be considered as positive. Therefore, the specific latent heat of fusion used in the calculation should be 79.7 cal/g or 330,000 J/kg for melting.
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