A mass of 5 kg of water is heated with a 500 W heater for 20 minutes. (i) Calculate the heat supplied. (ii) Determine the change in temperature. (iii) Explain why water is used as a cooling liquid.

The heat supplied by the heater is $\boxed{600000 \text{ J}}$.

(ii) Given that the specific heat capacity of water is $4200 \text{ J kg}^{-1} \text{K}^{-1}$, determine the change in temperature of the water during this time.

We have $Q = 600000 \text{ J}$ (from part i), $m = 5 \text{ kg}$, and $c = 4200 \text{ J kg}^{-1} \text{K}^{-1}$.

The change in temperature of the water is approximately $\boxed{28.57 \text{ K}}$.

(iii) Explain why water is often used as a cooling liquid in car radiators.
Water is often used as a cooling liquid in car radiators because it has a high specific heat capacity. This means it can absorb a large amount of heat energy from the engine without a significant rise in its own temperature, effectively cooling the engine.

7. (f) A student used an un-calibrated thermometer in the laboratory to measure the temperature of a given liquid. He first put it in pure melting ice and the mercury thread was $10 \text{ cm}$ long. He then removed it and put it in steam from boiling water, the mercury thread was $50 \text{ cm}$ long. Then he puts it in the liquid and the mercury thread was $35 \text{ cm}$ long.

(i) Define temperature.
Temperature is a measure of the average kinetic energy of the particles (atoms or molecules) within a substance, indicating its degree of hotness or coldness.

(ii) State two properties that make mercury suitable for use in thermometers.

1. Mercury has a uniform and visible expansion over a wide range of temperatures.
2. It has a high boiling point and a low freezing point, allowing it to measure a broad range of temperatures in liquid form.
3. It is a good conductor of heat, allowing it to quickly respond to temperature changes. (Any two of these are suitable).

(iii) Calculate the temperature of the liquid.

Length at $0^\circ C$ (melting ice), $L_0 = 10 \text{ cm}$.
Length at $100^\circ C$ (boiling water), $L_{100} = 50 \text{ cm}$.
Length in the liquid, $L_x = 35 \text{ cm}$.

The temperature of the liquid is $\boxed{62.5^\circ C}$.