Question

A substance is in the form of a solid at \[0^{\circ}\text{C}\]. The amount of heat added to this substance and the temperature of the substance are plotted on the following graph: 

If the specific heat capacity of the solid substance is \[500\ \text{J kg}^{-1}\ ^{\circ}\text{C}^{-1}\], find from the graph:

1. the mass of the substance;
2. the specific latent heat of fusion of the substance in the liquid state.

Answer 1

Given: Specific heat capacity of the solid,

\[c = 500\ \text{J kg}^{-1}\text{K}^{-1}\]

From the graph:

Heat supplied to raise the temperature from 0°C to 80°C = 800 J

Heat supplied during melting = \(1600-800=800\,\text{J}\)

Heat supplied to warm the solid,

\[Q = 800\ \text{J}\]

(i) Let the mass of the substance:

\[Q = mc\Delta T\]

\[ 800=m\times500\times(80-0) \]

\[ 800=m\times500\times80 \]

\[\therefore m = \frac{800}{500 \times 80}\]

\[\therefore m = \frac{800}{40000}\]

\[\therefore m = 0.02\ \text{kg}\]

(ii) Let the specific latent heat of fusion:

\[Q = mL\]

\[800 = 0.02 \times L\]

\[\therefore L = \frac{800}{0.02}\]

\[\therefore L = 40000\ \text{J kg}^{-1}\]