PHY C11: Temperature

This one is mainly definitions & measurements:

  • What is Temperature?
  • Thermometers
    • Thermometric Substances
    • Thermometric Properties
  • Empirical Calibration of a Thermometer
  • Absolute Scale / Thermodynamic Scale
  • Types of Thermometers

What is Temperature?
A measure of the degree of ‘hotness’ of a body. It is NOT the amount of thermal energy a body possesses.*

*Might revisit this, I’m not satisfied with this definition

Why is Temperature important?
t tells us how thermal energy will flow between 2 objects.

  • Thermal energy will flow from an object at a higher temperature to an object at a lower temperature, until they both reach the same temperature.
  • 2 objects at the SAME temperature will NOT have a net flow of thermal energy between them. They are in THERMAL EQUILIBRIUM.

How do you measure temperature?
Using a thermometer, an instrument for measuring temperature.

A thermometer uses thermometric substances which changes their thermometric properties according to their temperature.

Thermometric SubstanceThe working material of a thermometer, which has varying properties according to temperature.

Thermometric PropertyThe property of a substance which varies according to temperature.

Length of liquid thread in a tube
Electrical resistivity/conductivity

How do you empirically determine a temperature scale?
Empirical scale of temperature: a temperature scale which is determined EXPERIMENTALLY for a specific thermometer.

Compare the reading of the thermometer at FIXED POINTSFixed points: known reference temperatures where physical processes (such as state changes) occur.

The most common fixed points are the ICE POINT (0°C) and the STEAM POINT (100°C).

Thus, we can take a reading on my new thermometer at these 2 points.
Divide the difference between fixed points into equal intervals (degrees)If you divide the difference between the ice & steam points into 100 points, you get a CENTIGRADE scale (aka the Celsius scale).

However, I can just as easily divide it into 200 points or 50 or 2 or 1 – it’s completely arbitrary (though not always useful)!

In a general formula:

θ = k(Pθ – Plower)/(Pupper – Plower)

where P is the value of any thermometric property (pressure, volume, length, resistance, emf, etc.)

For the Celsius scale, we use the ice point (Pi) & steam point (Ps):

θ = 100(Pθ – Pi)/(Ps – Pi)

To recap: an EMPIRICAL temperature scale depends on the properties of thermometric substance. The value of 0 here is completely arbitrary. However, scientists require a universal scale: an ABSOLUTE SCALE or THERMODYNAMIC SCALE.

What is an absolute temperature scale?
A scale independent of a thermometric property. It defines 0 as the same for ALL thermometers. Thus, 0 must be the ABSOLUTE coldest temperature possible in the universe.

We call this scale the KELVIN SCALE (with units of K), & 0K is known as ABSOLUTE ZERO.

0K = -273.15°C

Now for some standardisations. This is all arbitrary (as long as 0K is absolute zero, an absolute scale is valid), but it’s useful for scientists to agree on a scale.

How is the Kelvin internationally defined?
Using GAS PRESSURE, interestingly.
For an ideal gas,
pV/T = constant

Here T is the ABSOLUTE or thermodynamic temperature. If we can keep V constant & measure p across different temperatures, we have a reliable method of defining T!

A CONSTANT-VOLUME GAS THERMOMETER is used to do exactly this.

Now we must identify our fixed points:

  • Lower Fixed Point: absolute 0 (0K, -273.15°C)
  • Upper Fixed Point: the triple point of water, 0.01°C

We don’t use the ice point (0°C) or the steam point (100°C) since these actually vary depending on atmospheric pressure. The triple point only occurs at a very specific pressure at 0.01 C, so it’s useful for defining the absolute temperature scale. Click here to find out more about the triple point.

Using our previous equation to define any temperature scale,
θ = k(Pθ – Plower)/(Pupper – Plower)
T = 273.16(pθ – 0)/(ptr – 0)

T = 273.16p/ptr

where T = temperature in Kelvin

This gives us the definition of a Kelvin:

One kelvin is the fraction 1/273.16 of the thermodynamic temperature of the triple point of water.

Converting between the Kelvin & Celsius scales
θ/°C = T/K – 273.15

Types of thermometers

TypeWorking PrincipleAdvantagesDisadvantages
GasExpansion of gas with temperature (pV = nRT)Most accurate to the thermodynamic scaleLarge/bulky

Unsuitable to measure small objects

Not suitable for rapidly varying temperatures
Liquid-in-glassExpansion of a liquid with temperatureConvenient, sensitive, moderately quick-acting

Accurate to thermodynamic temperature within range
Only operates within specific range (MP and BP of liquid)

Cannot be read from a distance through a display
Metal resistorResistance of a metal increases with temperature (not always linear)Wide range

Can be read from a distance through a display  
Inaccurate over wide range since variation is non-linear

Requires multiple calibration over different ranges
ThermistorsSemiconductor which has decreasing resistance with increasing temperature

AKA negative temperature coefficient (NTC)
Wide range

Small size

Fast response time

Can be read from a distance through a display

App: Used in car radiators
Not always linear, requires calibration

Power supply needed
ThermocoupleThermoelectric effect:

2 different metals release different number of electrons at a temperature, creating an emf between them.
Wide range

Very small size

Very fast response time

Can be read from a distance through a display

No power supply needed

Can measure temperature difference between 2 points

One thought on “PHY C11: Temperature

  1. Pingback: PHY C21: Outputs of Op-Amp Circuits – ProDuckThieves

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