CAIE A-Level Physics A2 14.3.1 Specific…Capacity

[Maximum number: 15]

Fig. 1.1 shows a small solid metal cylinder of mass m, length L and diameter d.

Fig. 1.1

The cylinder is heated to a uniform temperature. The cylinder is then removed from the heat source and the cylinder is wrapped in an insulating material.

The temperature of the room is $T_{\mathrm{R}}$ . At time t after the cylinder starts to cool, the surface temperature of the cylinder is $T_{\mathrm{C}}$ .

It is suggested that $T_{\mathrm{C}}$ is related to t by the relationship

\left(T_{\mathrm{C}}-T_{\mathrm{R}}\right)=Z \mathrm{e}^{-\frac{U A t}{m c}}

where A is the total surface area of the cylinder, c is the specific heat capacity of the metal, and U and Z are constants.
Plan a laboratory experiment to test the relationship between $T_{\mathrm{C}}$ and t.
Draw a diagram showing the arrangement of your equipment.
Explain how the results could be used to determine values for U and Z.
In your plan you should include:
- the procedure to be followed
- the measurements to be taken
- the control of variables
- the analysis of the data
- any safety precautions to be taken.
Diagram

Defining the problem

t is the independent variable and $T_{\mathrm{c}}$ is the dependent variable or vary t and measure $T_{\mathrm{c}}$

keep $T_{\mathrm{R}}$ constant

Methods of data collection

labelled diagram of workable experiment including:

- solid cylinder cooling

- insulation surrounding all of the cylinder

- thermometer touching cylinder inside insulation

- insulation and thermometer labelled

method to heat the cylinder uniformly, e.g. place in oven/immerse in hot water or diagram showing cylinder in oven or hot water

method to determine time t, e.g. stopwatch or temperature sensor connected to a data logger

method to measure L e.g. use a ruler/calipers/micrometer and method to measure d e.g. use calipers/micrometer

Method of Analysis

plot a graph of $\ln \left(T_{\mathrm{C}}-T_{\mathrm{R}}\right)$ against t or equivalent

$U=-\frac{m c \times \text { gradient }}{A}$ $Z=\mathrm{e}^{y \text {-intercept }}$

1

Additional detail including safety considerations

D1 precaution to prevent burns or use of hot cylinder / oven / hot water e.g. use of gloves, use of tongs

D2 keep thickness of the insulating material constant (for each $T_{\mathrm{C}}$ )

D3 method to measure m, e.g. use a (top-pan) balance

D4 for water bath/oven methods, wait for initial temperature of the cylinder to become uniform or constant throughout the cylinder

D5 (surface) $A=\pi d L+\frac{\pi d^{2}}{2}$ or $\pi d L+2\left(\frac{\pi d^{2}}{4}\right)$

D6 repeat measurements of d along the length of the cylinder / in different directions and determine the average value of d

D7 description of how c is determined from a separate experiment by heating the cylinder using electrical heater and
$c=\frac{\Delta E}{m \Delta \theta}$

D8 method of determining energy supplied to electrical heater to determine c, e.g. use of joulemeter for $\Delta E$ or electrical method using ammeter and voltmeter to determine I V t

D9 use several temperature sensors and determine the average $T_{\mathrm{C}}$

D10 relationship valid if a straight line is produced (with y-intercept $=\ln Z$ )

Do not accept line passing through the origin.

CAIE A-Level Physics A2 14.3.1 Specific Heat Capacity Topic Practice

Question 1