Explain thermometric property, determine temperature from a graph, and list methods of heat transmission.

At $0^\circ \text{C}$, the length L is $10 \text{ mm}$.
The value of the thermometric property at ice point is $\boxed{\mathbf{10 \text{ mm}}}$.

7. a) iii)

At $L = 30 \text{ mm}$, the temperature $\theta$ is $100^\circ \text{C}$.
The temperature $\theta$ is $\boxed{\mathbf{100^\circ \text{C}}}$.

7. b) i) Three methods by which heat can be transmitted are:

• Conduction
• Convection
• Radiation

7. b) ii)

• Diagram of setup: Place several rods of different materials (e.g., copper, iron, glass) of identical length and cross-sectional area side-by-side. Attach a small piece of wax or a thumbtack with wax to the far end of each rod.
• Procedure: Heat the other ends of all the rods simultaneously using a single heat source (e.g., a Bunsen burner flame applied to a common metal plate touching all rods, or by immersing the ends in a hot water bath).
• Observations: Observe the order in which the wax pieces melt and fall off the rods. The wax on the copper rod will melt first, followed by iron, and then glass.
• Conclusion: This shows that different materials conduct heat at different rates, with copper being a better conductor than iron, and iron better than glass.
• Precaution: Ensure all rods have the same dimensions and are heated equally at the starting end.

7. c) The statement means that $4,200 \text{ Joules}$ of heat energy are required to raise the temperature of $1 \text{ kilogram}$ of water by $1 \text{ Kelvin}$ (or $1^\circ \text{C}$).

8. a) i) Density is defined as the mass per unit volume of a substance.

8. a) ii) Two factors that affect the density of a solid are:

• Temperature
• Type of material (composition/atomic structure)

8. b) i) Hooke's Law states that the extension of a spring or elastic material is directly proportional to the applied force, provided the elastic limit is not exceeded.

8. b) ii)
A graph of Force / N (y-axis) against Extension / cm (x-axis) would show:

• A straight line passing through the origin for the initial points (0,0), (1.5,20), (3.1,40), (4.3,60).
• The line might start to curve slightly for higher forces (e.g., 80 N and 100 N), indicating that the elastic limit might be approached or exceeded, or due to measurement variations.

8. b) iii)

Using the data points (0,0), (1.5,20), (3.1,40), and (4.3,60), we can calculate the slope of the best-fit line.
Using linear regression for these points:
Slope $m = \frac{n(\sum xy) - (\sum x)(\sum y)}{n(\sum x^2) - (\sum x)^2}$
For x = [0, 1.5, 3.1, 4.3] and y = [0, 20, 40, 60]:
$\sum x = 8.9$
$\sum y = 120$
$\sum x^2 = 0^2 + 1.5^2 + 3.1^2 + 4.3^2 = 0 + 2.25 + 9.61 + 18.49 = 30.35$
$\sum xy = (