Heat

We all have an idea of what we mean by ‘hot’ or ‘cold’. To give a numerical value to just how hot or cold something is we introduce the idea of a ‘scale of temperature’. We make use of the observation that certain physical quantities are affected by heat – for example, most liquids expand when heated and contract when cooled.

To establish a temperature scale we:

1. Choose a property of something that varies continuously with its degree of hotness (called a thermometric property)
2. Choose two standard degrees of hotness and assign numerical values to them
The Celsius scale of temperature

On this scale:

1. The lower fixed point is the ice-point. This is the temperature of pure ice melting under standard atmospheric pressure (76cm Hg) and is defined as zero degrees Celsius (00C)
2. The upper fixed point is the steam-point. This is the temperature of steam coming from water boiling under standard atmospheric pressure, and is defined as 1000C
The thermometric property may be the length of a mercury (‘Hg’) thread in a glass stem or the resistance of a piece of wire etc. To be general for now, let:

1. Mercury in glass thermometer

Mercury is a metal, but is unusual in being a liquid at room temperature. It expands when heated and contracts when cooled. It moves along the capillary of the thermometer when the temperature changes. It does not stick to the glass and is easily visible. Mercury freezes at –390C and so for temperatures below this, coloured alcohol is used.

In this case the thermometric property is the length (L) of the mercury thread.

So, in the defining equation: X è L

Calibrating a mercury thermometer

To calibrate a thermometer means to put a temperature scale on it.

The following set-ups can be used to establish the ice-point and steam-point (diagrams not drawn to scale):

With the ice steadily melting the ice-point is marked on the stem of the thermometer.

With steam steadily escaping from the steam-chest the steam-point is marked on the stem. Care should be taken to avoid getting burned. The water need only be simmering, to avoid steam building up quicker than it can escape.

The thermometer is removed, and then the gap between the two marks divided into 100 equal interval, from  00C to 1000C. It can then be used to measure unknown temperatures.

Why use pure, melting ice? Pure ice is used because impurities in ice change its melting point. Also, we wait for the ice to be melting since, when ice is taken directly from the freezer, it can be well below its freezing point, but it melts on its surface at its melting point.

Why use steam instead of boiling water? The boiling point of water depends on its purity. The steam coming from water will be purer than the water it escapes from and will be at the boiling point of pure water.

Using the formula

L0 = 0, i.e. measurements are made from the ice-point mark on the stem.

2. Constant volume gas thermometer (not drawn to scale)

The above set-up is quite fragile, and contains a lot of mercury. It is therefore usually attached securely to a stable support. The right-hand side can be raised or lowered to keep the mercury in the left side at the constant reference level R, thus ensuring that the volume of the gas is constant each time a value of height difference h is recorded.

The pressure of the gas = H + h.
In the position shown, h is positive. It is negative if the Hg in the right side is below R.
The mass of the gas is constant, since none can escape.

Here pressure, P, can be used as a thermometric quantity.

In the defining equation: X è P

Example

In an experiment to measure room temperature with the above set up:

3. Thermocouple thermometer

If two different metals form a circuit, as represented below, with their junctions at different temperatures, then a current flows.

The pair of metals form a thermocouple, and the current is called a thermoelectric current. The current is produced by an induced electromotive force (‘emf’- a voltage). The phenomenon is called the Seebeck effect.

In the defining equation: X è E
In the above graph, the change in E for a given change in temperature gets less and less as the neutral temperature is approached. Thus, a thermocouple thermometer is not usually used to measure temperatures close to its neutral temperature, since it is not very sensitive to temperature change in this region.

In practical thermocouple thermometers, the cold junction is usually kept at a constant temperature, and the hot junction is used to determine an unknown temperature. The junction can be very small, so is has a small heat capacity, and so has little effect on the temperature being measured. Also, a thermocouple thermometer can respond rapidly to a changing temperature.

4. Platinum resistance thermometer

The electrical resistance, R, of a piece of wire varies with temperature, and so R can be used as a thermometric property.

In the defining equation: X è R

Example

A piece of platinum wire has resistance 2.8 ohms at the steam-point and 2.4 ohms at 500C. What is its resistance at the ice-point?

5. Thermistor

The term thermistor comes from thermal resistor. As the name suggests, it is a device whose resistance depends on its temperature, and so it can be calibrated to measure temperature.

A thermistor is a semiconductor. One commonly used type is an NTC type ('Negative Temperature Coefficient'), for which resistance falls significantly as the temperature rises. When such a thermistor is heated, more electrons are liberated from their bonds and are free to then act as current carriers, hence the drop in resistance.

A circuit such as the following can be used to determine the resistance of a thermistor at various temperatures:

The thermistor would be coated in varnish to make it water resistant, and then immersed in water which would be gradually heated. The resistance (R = V/I) could be determined over a range of temperatures - for example, the thermistor could be initially be placed in ice-water which is then gradually heated to boiling.

A graph of R against temperature can be plotted, which is a 'calibration graph' for the thermistor over the temperature range used:

If the thermistor were placed in a substance at an unknown temperature, from its resistance, the temperature could be found from the calibration graph.

As a practical thermometer, a thermistor would be connected to a resistance meter calibrated to read directly in 0C.

Advantages of a thermistor over a liquid-in-glass thermometer include:

1. it is less easily broken
2. it can be placed remotely from the observer (the connecting wires can be made longer)

Temperature ranges

The range of the gas thermometer depends upon the gas used. For very low temperatures, helium is used.

Disagreement between thermometers

The above thermometers:

• are bound to give the same readings at the fixed points (i.e. at the ice-point and steam-point)
• may not give exactly the same readings at any other temperature
The equation used above to define the Celsius scale is linear:
Suppose that a mercury thermometer is placed in a substance and the Hg thread comes to rest exactly half way between the ice-point and steam-point marks. In terms of the above defining equation, this implies a temperature of 500C.

However, if a resistance thermometer were put in the same substance, its resistance is not bound to be exactly half way between its values at the ice-point and the steam-point, and so the defining equation would not give exactly 500C.