Question

A substance in the form of a solid at 0°C. The amount of heat added to this substance and the temperature of the substance are plotted on the given graph. If the specific heat capacity of the solid is 0.5 J g⁻¹°C⁻¹, find from the graph

1. Mass of the substance.
2. The specific latent heat of fusion of the substance in the liquid state.

Answer 1

From the graph, the solid is heated from 0°C to its melting point 80°C.

Heat absorbed in this part is Q₁ = 800 J

During fusion the temperature stays at 80°C; heat absorbed in the horizontal part is Q₂ = 3600 − 800 = 2800 J

(i) Q₁ = mcΔT

$$m = \frac{Q_1}{c \Delta T}$$

$$= \frac{800}{0.5 \times 80}$$

= 20 g

(ii) Q₂ = mL

$$L = \frac{Q_2}{m}$$

$$= \frac{2800}{20}$$

= 140 J g⁻¹

= 1.4 × 10⁵ J kg⁻¹

Therefore, the mass of the substance is 20 g, and the specific latent heat of fusion is 140 J g⁻¹ (or 1.4 × 10⁵ J kg⁻¹).