Question

A solid metal weighting \[150g\] melts at its melting point of ${800^0}C$ by providing heat at the rate of \[100W\]. The time taken for it to completely melt at the same temperature is \[4{\text{ }}min\]. What is the specific latent heat of fusion of the metal?

Answer 1

Hint: This problem can be solved by good knowledge of specific heat capacity and latent heat capacity. Latent heat capacity is energy required to break inter- atomic attraction forces and make it possible to change the state of matter(without changing its temperature) like Ice to water or liquid to gas.

Formula used:
Latent heat capacity :- energy required to break inter- atomic attraction force and make it possible to change the state of matter(without changing its temperature) like Ice to water or liquid to gas.
Here heat Transfer \[Q\left( J \right)\], mass of metal \[m\left( {kg} \right)\] and specific latent heat capacity \[L\left( {J/kg} \right)\]
Heat required = mass of metal $\times$ specific latent heat capacity
$Q(J) = m(kg) \times L(J/kg)$

Complete step by step answer:
First let us know about the
Specific heat capacity :- Energy required to raise the temperature of 1 kg of substance by 1 Kelvin.
Latent heat capacity :- energy required to break inter- atomic attraction force and make it possible to change the state of matter(without changing its temperature) like Ice to water or liquid to gas.
 Latent heat of fusion:- heat energy required to convert from solid to liquid at atmospheric pressure.
Here heat Transfer \[Q\left( J \right)\], mass of metal \[m\left( {kg} \right)\] and specific latent heat capacity \[L\left( {J/kg} \right)\]
Heat required = mass of metal $\times$ specific latent heat capacity
$Q(J) = m(kg) \times L(J/kg)$
Given :-
$
  m = 150g = 150 \times {10^{ - 3}}kg = 0.15kg \\
  power(P) = 100W \\
  Time(t) = 4\min = 240\sec \\
 $
The amount of heat supplied in 4 min
Heat energy = power × time
                      = $P \times t$
            = $100 \times 240$=24000 joules
Let L be the latent specific heat
Then
$Q(J) = m(kg) \times L(J/kg)$
$24000 = 0.15 \times L$
$L = \dfrac{{24000}}{{0.15}} = 16 \times {10^3}J/kg$
Hence the specific heat of fusion \[ = 16 \times {10^3}J/kg\]

Note:
The best way to solve these problems is good command in conversion of heat at the time of change in state without change of temperature. It can be possible to understand about the latent heat and its relation with other forms of energy. You should have good command in the concept as well as formula related to the concept.