a) Hooke's Law states that the extension of a spring is directly proportional to the force applied to it, provided the elastic limit is not exceeded. b) The proportionality constant of the spring, also known as the spring constant ($k$), is given by the ratio of the applied load (force, $F$) to the extension ($x$). $$k = \frac{F}{x}$$ Step 1: Choose a point from the linear portion of the graph. From the graph, when the Load ($F$) is $1 \text{ N}$, the Extension ($x$) is $5 \text{ cm}$. Step 2: Convert the extension from centimeters to meters to use SI units for the spring constant. $$x = 5 \text{ cm} = 0.05 \text{ m}$$ Step 3: Calculate the spring constant $k$. $$k = \frac{1 \text{ N}}{0.05 \text{ m}} = 20 \text{ N/m}$$ Using another point, for example, when Load ($F$) is $4 \text{ N}$, Extension ($x$) is $20 \text{ cm}$. $$x = 20 \text{ cm} = 0.20 \text{ m}$$ $$k = \frac{4 \text{ N}}{0.20 \text{ m}} = 20 \text{ N/m}$$ The proportionality constant of the spring is $\boxed{\text{20 N/m}}$. c) Two factors that affect the proportionality constant of a vertical spring are: • The material of the spring (e.g., steel, copper). • The diameter of the wire used to make the spring. d) i) Given that the $L_v$ is the specific latent heat of vaporization of steam. ii) The latent heat of vaporization ($Q$) is the total energy required to change the state of a mass $m$ of a substance at its boiling point without a change in temperature. Given $L_v$ is the specific latent heat of vaporization (energy per unit mass), the expression for the total latent heat of vaporization is: $$Q = mL_v$$ where $m$ is the mass of the steam and $L_v$ is the specific latent heat of vaporization. The expression for the latent heat of vaporization of steam is $\boxed{Q = mL_v}$.