# 86-Q2: Newton’s Law of Cooling¶

Time 1$$\frac{1}{2}$$ hr.

## Apparatus¶

Thermometer ($$0-100\text{°C}$$); calorimeter (very small capacity), with lid & stirrer; cardboard base; stopclock; supply of boiling water; 2 sheets graph paper; clamp & stand.

The aim of this experiment is to investigate the manner in which a calorimeter containing hot water cools down.

## Procedure¶

Pour the boiling water into the calorimeter until it is about three-quarters full, and then set up the calorimeter as illustrated below. Carefully observe and record the temperature $$\Theta\text{°C}$$ of the water inside the calorimeter after every two minutes. Continue the process while stirring the calorimeter until the temperature of the water drops to about $$50\text{°C}$$.

1. Tabulate the values of $$\Theta$$ (in °C) and the corresponding values of time $$t$$ (in minutes), starting at $$t=0$$. Also measure and record the room temperature $$\Theta_R$$. (marks 8,4)
2. Plot the cooling curve for the calorimeter and its contents using the table in (a) above. (10 marks)
3. Choose six points ($$\Theta$$, $$t$$) along the curve in (b) above and at each point draw the tangent to the curve and then determine the gradient $$G$$ of the curve at that point. Calculate and record the excess temperature ($$\Theta - \Theta_R$$) corresponding to each of the six points chosen. Hence make up a table that consists of values of $$G$$ with corresponding values of ($$\Theta - \Theta_R$$). (marks 3,6,3)
4. Using the results of (c) above, draw a graph of “Rate of cooling” vs. “Excess temperature.” (10 marks)
5. Compare the results of (d) above with Newton’s Law of Cooling and make any relevant comments. (6 marks)