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.

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

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