◼ measure the mass, m, in kg of the substance under test using electronic scales
◼ measure the initial temperature and the final temperature, using a thermometer to find Δθ °C
◼ determine the amount of thermal energy supplied – this is usually done with an electric immersion heater
as shown below. low voltage power supply
Apparatus for measuring the specific heat capacity of a substance
Figure shows typical apparatus for finding the s.h.c. of a metal. A cylinder of the metal is drilled to allow an
electric heater and a thermometer to be inserted as shown. Use a balance to find the mass of the cylinder
and a thermometer to measure its temperature. Turn the heater on and measure the voltage, V (volts),
supplied to the heater, the current drawn, I (amps), and the length of time, t (seconds), the heater is on.
Make a note of the highest temperature reached and calculate Δθ, the rise in temperature. The thermal
energy supplied by the heater is ΔQ = V × I × t . Substitute the measured values for m, ΔQ and Δθ into the
equation shown above and calculate the s.h.c. The insulation is used to cut down heat losses to the
surroundings.
This method can be used to measure the s.h.c. of water, with a weighed amount (m) of water in beaker
(with a lid and insulation). The water can be heated with an immersion heater and heat energy given to the
water calculated in the same way (ΔQ = VIt). The temperature increase is measured with a thermometer.
Figure 2.13a shows apparatus that may be used to investigate the relationship between the force applied to
a spring and its extension. The length of the unstretched spring is measured with a half-metre rule then the
spring is loaded with different weights. The extension for each load is measured against a scale using a set
square to improve measurement accuracy. A table of results is recorded and a graph of load force against
extension plotted as shown in Figure 2.13b. The extension measurements can be checked by unloading
the weights one at a time and remeasuring the extension for each load.
Here the result is a straight line graph passing through the origin of the axes. The spring obeys Hooke’s
law.
Hooke’s law only applies if you do not stretch a spring too far. Figure 2.14 shows what happens if you
stretch a spring too far. You can see that the line starts to curve at a point called the limit of proportionality.
This is the point where the spring stops obeying Hooke’s law and starts to stretch more for each increase in
the load force. If the load is increased more, a point called the elastic limit is reached. Once you have
stretched a spring beyond the elastic limit it will not return to its original length as you take the weights off
the spring.
Hooke’s law also applies to wires. If you stretch a wire, you will find that the extension is proportional to the
load up to a certain load then it may behave as the spring shown in Figure 2.14. Wires made of different
metals will behave in different ways – some will obey Hooke’s law until the wire breaks; other types of metal
will stretch elastically and then plastically before breaking.
If you stretch an elastic
band with increasing load forces, you get a graph like that shown in Figure 2.16. The graph is not a straight
line, showing that elastic bands do not obey Hooke’s law.
1 Shine a ray of light onto one of the sides of the glass block, so that the ray emerges on the opposite side
of the block. Mark the directions of both of these rays with crosses.
2 Draw around the glass block before removing it.
3 Using the crosses, draw in the direction of both rays.
4 Draw in the direction of the ray that travelled inside the glass block.
5 Draw a normal (a line at 90° to the glass surface) where the ray enters the block.
6 Measure the angles of incidence (i) and refraction (r).
7 Use the equation n = sin i / r to find the refractive index of the glass block
a A semi-circular glass block used to demonstrate total internal reflection b Light striking the edge of the
glass block at the critical angle
As shown in Figure 12.12a, a ray of light is directed at the centre of the straight side of the block through
the curved side. (We do this because the incident ray will then always hit the edge of the glass block at 90°,
so there are no refraction effects to take into account as the light goes into the block.) Now by carefully
increasing and decreasing the angle at which the ray strikes the flat edge of the glass block, we can
discover the smallest angle at which most of the light is refracted along the edge of the glass block (see
Figure 12.12b). This angle is the critical angle.
One of the most important applications for total internal reflection is the optical fibre. This is a very thin
piece of fibre composed of two different types of glass. The centre is made of a glass that has a high
refractive index surrounded by a different type of glass that has a lower refractive index.
In an optical fibre, light undergoes total internal reflection.
As the fibres are very narrow, light entering the inner core always strikes the boundary of the two glasses at
an angle that is greater than the critical angle. No light escapes across this boundary. The fibre therefore
acts as a ‘light pipe’ providing a path that the light follows even when the fibre is curved. Large numbers of
these fibres fixed together form a bundle. Bundles can carry sufficient light for images of objects to be seen
through them. If the fibres are tapered (narrower at one end) it is also possible to produce a magnified
image. Figure 12.22 shows optical fibres in an endoscope. The endoscope is used by doctors to see the
inside the body – for example, to examine the inside of the stomach. Endoscopes can also be used by
engineers to see hard-to-reach parts of machinery. Light travels down one bundle of fibres and shines on
the object to be viewed. Light reflected by the object travels up a second bundle of fibres. An image of the
object is created by the eyepiece.
By using optical fibres to see what they are doing, doctors can carry out operations through small holes
made in the body, rather than through large cuts. This is called ‘keyhole surgery’. This is less stressful for
patients and usually leads to a more rapid recovery.
Optical fibres are used in endoscopes to see inside the body
Modern telecommunications systems use optical fibres rather than copper wires to transmit messages as
less energy is lost. Electrical signals from a telephone are converted into light energy produced by tiny
lasers, which send pulses (small amounts) of light into the ends of optical fibres. A light-sensitive detector at
the other end changes the pulses back into electrical signals, which then flow into a telephone receiver (ear
piece).
1 Set up the circuit shown in Figure 8.4. 2 Turn the variable resistor to its maximum value. 3 Close the
switch and take the readings from the ammeter and the voltmeter. 4 Alter the value of the variable resistor
again and take a new pair of readings from the meters. 5 Repeat the whole process at least six times. 6
Place the results in a table (see the table below) and draw a graph of current (I) against voltage (V).
▲ Figure 8.4 This circuit can be used to investigate the relationship between current and voltage.
▲ Typical results table
▲ Figure 8.5 Graph of results
The graph in Figure 8.5 is a straight line graph passing through the origin. The slope of the graph tells us
about the resistance of the wire. The steeper the slope the smaller the resistance of the wire. If we repeat
this experiment for other components, such as a resistor, a filament bulb and a diode, the shapes of the
graphs we obtain are often very different to that shown in Figure 8.5. By looking very carefully at these
shapes we can see how they behave.
▲ Figure 8.6 The graph is a straight line. It has a constant slope. So the resistance of this component does
not change.
▲ Figure 8.7 This graph is not a straight line. The resistance of the bulb changes. At higher currents and
voltages the slope of the graph shows us that the resistance of the filament bulb increases – that is, as the
temperature of the filament increases the current decreases.
▲ Figure 8.8 This strangely shaped graph shows that diodes have a high resistance when the current is in
one direction and a low resistance when it is in the opposite direction (see page 81).
▲ Figure 8.14 Two examples of thermistors and their symbol – the resistance of a thermistor changes a lot
as the temperature changes.
A thermistor is a resistor whose resistance changes quite a lot even with small changes in temperature.
▲ Figure 8.13 A graph showing a thermistor’s decreasing resistance with increasing temperature
Thermistors are used in temperature-sensitive circuits in devices such as fire alarms. They are also used in
devices where it is important to make sure there is no change in temperature, for example, in freezers and
computers.
▲ Figure 8.16 Light-dependent resistor
A light-dependent resistor (LDR) has a resistance that changes when light is shone on it. In the dark its
resistance is high but when light is shone on it its resistance decreases.
Figure 8.15 A graph showing an LDR’s decreasing resistance with increasing light intensity LDRs are often
used in light-sensitive circuits in devices such as photographicexposure equipment, automatic lighting
controls and burglar alarms.