CAIE A-Level Physics A2 14 Temperature Questions

Practise analysing thermal equilibrium and temperature scales, evaluating thermometers and calculating heating, phase-change and energy-transfer quantities.

Exam points

analyse temperature measurement, thermal equilibrium and energy transfer
convert and interpret thermodynamic temperature scales, including absolute zero
calculate energy changes using specific heat capacity and specific latent heat
distinguish sensible heating from phase-change energy and interpret experimental data

Covered syllabus points

14.1 Thermal equilibrium 14.2 Temperature scales 14.3 Specific heat capacity and specific latent heat

[Maximum number: 10]

Use the information in (i) to draw, on Fig. 1.1, a line to represent the temperature of the block, assuming no energy losses to the surroundings.

(a)

State

[ 2 ]

(i)

what may be deduced from the difference in the temperatures of two objects,

[ 1 ]

(ii)

the basic principle by which temperature is measured.

[ 1 ]

(b)

By reference to your answer in (a)(ii), explain why two thermometers may not give the same temperature reading for an object.

[ 2 ]

(c)

A block of aluminium of mass 670 g is heated at a constant rate of 95 W for 6.0 minutes. The specific heat capacity of aluminium is $910 \mathrm{Jkg}^{-1} \mathrm{~K}^{-1}$ . The initial temperature of the block is $24^{\circ} \mathrm{C}$ .

[ 6 ]

(i)

Assuming that no thermal energy is lost to the surroundings, show that the final temperature of the block is $80^{\circ} \mathrm{C}$ .

[ 3 ]

$P t=m c(\Delta) \theta$ $95 \times 6 \times 60=0.670 \times 910 \times \Delta \theta$ $\Delta \theta=56^{\circ} \mathrm{C}$ so final temperature $=56+24=80^{\circ} \mathrm{C}$
or

$95 \times 6 \times 60=0.67 \times 910 \times(\theta-24)$
so final temperature or $\theta=80^{\circ} \mathrm{C}$

(ii)

In practice, there are energy losses to the surroundings. The actual variation with time t of the temperature $\theta$ of the block is shown in Fig. 1.1.

Fig. 1.1

[ 3 ]

1. sketch: straight line from (0,24) to (6,80)

2. temperature drop due to energy loss $=(80-64)=16^{\circ} \mathrm{C}$

energy loss $=0.670 \times 910 \times(80-64)=9800\,\mathrm{J}$

or

energy to raise temperature to $64^{\circ} \mathrm{C}=0.670 \times 910 \times(64-24)$ $=24400\,\mathrm{J}$ $\text{loss}=(95 \times 6 \times 60)-24400=9800\,\mathrm{J}$

[Maximum number: 6]

(a)

State the magnitude and unit of absolute zero on the thermodynamic temperature scale.

[ 1 ]

(b)

Explain why temperature measured using a laboratory liquid-in-glass thermometer does not give a measurement of thermodynamic temperature.

[ 1 ]

(c)

Fig. 2.1 shows a simplified diagram of a type of thermometer called a platinum resistance thermometer.

Fig. 2.1

The glass tube is immersed in the environment for which the temperature is to be determined. The resistance between the terminals X and Y is measured.

Fig. 2.2 shows the variation of the resistivity $\rho$ of platinum with thermodynamic temperature T.

Fig. 2.2

[ 4 ]

(i)

Explain how Fig. 2.2 shows that platinum is a suitable metal for use in a resistance thermometer.

[ 2 ]

(ii)

Suggest a reason why a platinum resistance thermometer is not suitable for measuring a rapidly changing temperature.

[ 1 ]

(iii)

Suggest a type of thermometer that is suitable for measuring a rapidly changing temperature.

[ 1 ]

[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.

[Maximum number: 8]

Fig. 2.1 shows a laboratory thermometer that is calibrated to measure temperature in degrees Celsius.

Fig. 2.1

The thermometer makes use of the fact that the density of mercury varies with temperature.

(a)

State two other physical properties of materials, apart from the density of a liquid, that can be used for measuring temperature.

1

2

[ 2 ]

(b)

The thermometer is initially at $23.0^{\circ} \mathrm{C}$ , as shown in Fig. 2.1. It is used to measure the temperature of an insulated beaker of water that is at $37.4^{\circ} \mathrm{C}$ . The bulb of the thermometer is inserted into the water, and the water is stirred until the reading on the thermometer becomes steady.

The mass of water in the beaker is 18.7 g .
The mass of mercury in the thermometer is 6.94 g .
The specific heat capacity of water is $4.18 \mathrm{~J} \mathrm{~g}^{-1} \mathrm{~K}^{-1}$ .
The specific heat capacity of mercury is $0.140 \mathrm{~J} \mathrm{~g}^{-1} \mathrm{~K}^{-1}$ .
The glass of the thermometer and the beaker containing the water can be considered to have negligible heat capacity.

[ 4 ]

(i)

Calculate, to three significant figures, the final steady temperature indicated by the thermometer in the water. ${ }^{\circ} \mathrm{C}$

[ 3 ]

$Q=m c \Delta T$
evidence of realisation that Q lost by water =Q gained by mercury
$18.7 \times 4.18 \times(37.4-T)=6.94 \times 0.140 \times(T-23.0)$ $T=37.2^{\circ} \mathrm{C}$

(ii)

Suggest one change that could be made to the design of the thermometer that would enable it to give a more accurate measurement of temperature.

[ 1 ]

(c)

Explain why the thermometer in Fig. 2.1 does not provide a direct measurement of thermodynamic temperature.

[ 2 ]

depends on properties of a real substance
$0^{\circ} \mathrm{C}$ is not absolute zero

All question bank results loaded

Covered syllabus points

Question 1

Question (a)

Question (i)

Question (ii)

Question (b)

Question (c)

Question (i)

Question (ii)

Question 2

Question (a)

Question (b)

Question (c)

Question (i)

Question (ii)

Question (iii)

Question 3

Question 4

Question (a)

Question (b)

Question (i)

Question (ii)

Question (c)