Answer: When a substance changes from a solid to a liquid (melting), the kinetic energy of the particles increases. The particles vibrate with greater amplitude and are able to move more freely. As the temperature rises, the particles overcome the strong intermolecular forces holding them in a fixed lattice structure.

Consequently, the distances between the particles increase. In the solid state, particles are held in fixed positions with very short distances. In the liquid state, particles are still relatively close, but they can move past each other, leading to longer distances between them compared to the solid state.

This change in kinetic energy and particle spacing directly relates to the properties of the substance:

• Solid: High kinetic energy is restricted, resulting in strong intermolecular forces and a fixed shape and volume.
• Liquid: Increased kinetic energy allows particles to move past each other, resulting in a fixed volume but no fixed shape (takes the shape of the container).

Given:

• Mass of gas (m) = constant
• Temperature (T) = 27°C = 300 K
• Initial volume (V₁) = 2.0 dm³
• Initial pressure (P₁) = 300 kPa

To find: New volume (V₂)

Equation: p V = constant

Calculation:

P₁ V₁ = P₂ V₂

300 kPa × 2.0 dm³ = P₂ × V₂

600 = P₂ × V₂

V₂ = 600 / P₂

Assume the pressure is increased to 400 kPa:

V₂ = 600 / 400 = 1.5 dm³

Answer: The new volume of the gas is 1.5 dm³ (assuming the pressure is increased to 400 kPa). The question does not specify the change in pressure, so the answer must include this assumption.

Explanation of the graph:

The graph shows a direct relationship between pressure and volume for a fixed mass of gas at a constant temperature. As the volume decreases, the pressure increases proportionally, and vice versa. This is because the number of gas molecules and their kinetic energy remain constant. Therefore, if the volume decreases, the molecules have less space to move and collide with the container walls more frequently, resulting in higher pressure. Conversely, if the volume increases, the molecules have more space and collide with the walls less frequently, resulting in lower pressure.

Effect of increasing temperature:

If the temperature was increased, the graph would shift upwards and to the right. This is because increasing the temperature increases the average kinetic energy of the gas molecules. The molecules would move faster and collide with the container walls more frequently and with greater force. To maintain the same pressure (p V = constant), the volume would need to increase to accommodate the higher kinetic energy of the molecules. The line on the graph would therefore be at a higher pressure and a higher volume for the same point on the x-axis (volume).