Which of the following best represents the temperature versus heat supplied graph for water, in the range of - 20 °C to 120 °C ?

The heating process for water from $$-20^\circ\text{C}$$ to $$120^\circ\text{C}$$ involves three distinct states of matter and two phase transitions.

1. Heating Ice ($$-20^\circ\text{C}$$ to $$0^\circ\text{C}$$)

Heat is initially supplied to raise the temperature of solid ice. The relationship is linear: $$Q = m \cdot s_{ice} \cdot \Delta T$$

Since the specific heat of ice $$s_{ice}$$ is approximately $$0.5 \text{ cal/g}^\circ\text{C}$$, the temperature rises with a relatively steep slope ($$\frac{dT}{dQ} = \frac{1}{ms}$$).

2. Melting Phase Change (at $$0^\circ\text{C}$$)

When the ice reaches its melting point, the temperature remains constant while the state changes from solid to liquid. This is represented by a horizontal plateau: $$Q = m \cdot L_f$$

Here, $$L_f = 80 \text{ cal/g}$$ is the latent heat of fusion.

3. Heating Liquid Water ($$0^\circ\text{C}$$ to $$100^\circ\text{C}$$)

After all ice has melted, the temperature of the liquid water rises: $$Q = m \cdot s_{water} \cdot \Delta T$$

The specific heat of water $$s_{water}$$ is $$1.0 \text{ cal/g}^\circ\text{C}$$. This section has a lower slope than the ice section because more heat is required to raise the temperature by one degree.

4. Boiling Phase Change (at $$100^\circ\text{C}$$)

At the boiling point, the temperature again remains constant during vaporization, creating a second horizontal plateau: $$Q = m \cdot L_v$$

Because the latent heat of vaporization ($$L_v = 540 \text{ cal/g}$$) is significantly higher than the latent heat of fusion, this plateau is much longer than the one at $$0^\circ\text{C}$$.

Graph (C) is the only representation that correctly shows:

The starting point below the origin ($$-20^\circ\text{C}$$).

Both phase change plateaus at $$0^\circ\text{C}$$ and $$100^\circ\text{C}$$.

A longer second plateau to account for the higher energy required for vaporization.

Hence, option (C) is correct.