The correct answer is D because:

The material changes from a solid to a liquid between times t₁ and t₂.
The amount of energy E required to melt a mass of m with latent heat L is:
- E = mL
Since m = 1 kg, L = E
E = Pt, where t is the duration of time the power is supplied.
So L = P(t₂ - t₁)

A is incorrect as when a substance changes state from solid to liquid, the internal energy will increase, since the potential energy of the molecules increases.

B is incorrect as when a substance changes state from solid to liquid, the kinetic energy of the molecules does not change.

C is incorrect as the specific heat capacity of the liquid state is lower than the specific heat capacity of the solid state. This is because less time, and therefore less energy is required to raise the temperature of the liquid by any given amount.

To see mathematically how the specific heat capacity can be determined from the slope of a against t graph:
- $E = m c Δ θ$ and $E = P t$ so
- $m c ∆ θ = P t$
- gradient = $\frac{∆ θ}{∆ t}$ = $\frac{P}{m c}$
- So $c = \frac{P}{m \times g r a d i e n t}$
- If P and m are constant: c ∝ $\frac{1}{g r a d i e n t}$
- The larger the gradient, the lower the value of c.

Thermal Properties of Materials (OCR A Level Physics)

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