Question

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

Answer 1

Step 1: Given data

Mass of the solid metal $m=150g=0.15kg$

Heat rate $P=100W$

Time $T=4min=240s$

Step 2: Finding the total heat

Heat supplied $H=Pt$ where P is heat rate, t is time

$H=100\times 240=2.4\times {10}^{4}J$

Step 3: Finding the latent heat of fusion

Heat energy $H=mL$ where m is mass, L is the specific latent heat of fusion

Then specific latent heat of fusion $L=\frac{H}{m}$

On substitution:

$L=\frac{2.4\times {10}^{4}J}{0.15}$

$L=1.6\times {10}^{5}J/Kg$

Thus the specific latent heat of fusion of the metal is $1.6\times {10}^{5}J/Kg$.