Question

Find the specific latent heat of the melting process in $calk{g}^{-1}$

Answer 1

From the plot, melting occurs on the path AB where temp remains constant at ${80}^{0}C$ and amount of heat supplied is 800 calories.
Amount of heat supplied when temp rises from $0^{0}C$ to ${80}^{0}C$ is $Q=m\ast 0.5\ast 80$
$\therefore \frac{dQ}{dT}=mass\ast 0.5$ .....(2)
From the plot, $\frac{dQ}{dT}=\frac{1}{m}$ where m is the slope of the T-Q plot.
$\therefore \frac{dQ}{dT}=\frac{1}{\frac{80}{800}}=10$ .....(3)
Equating (2) and (3), we get $mass\ast 0.5=10$ $\therefore mass=20gms$
Thus, during melting 800 calories of heat is supplied for 20 gms of the solid substance.
$\therefore$ amount of heat supplied for 1 kg of solid substance is $L=800\ast \frac{1000}{20}=40000calk{g}^{-1}$