Measurement of Temperature
- A thermometer is any device that is used to measure temperature
- Each type of thermometer uses a physical property of a material that varies with temperature – examples of such properties include:
- The density of a liquid
- The volume of a gas at constant pressure
- Resistance of a metal
- e.m.f. of a thermocouple
- In each case, the thermometer must be calibrated at two or more known temperatures (commonly the boiling and melting points of water, $0^{\circ} \mathrm{C}$ and $100^{\circ} \mathrm{C}$ respectively) and the scale divided into equal divisions
The Density of a Liquid
- A liquid-in-glass thermometer depends on the density change of a liquid (commonly mercury)
- It consists of a thin glass capillary tube containing a liquid that expands with temperature
- A scale along the side of the tube allows the temperature to be measured based on the length of liquid within the tube
Volume of a Gas at Constant Pressure
- The volume of an ideal gas is directly proportional to its temperature when at constant pressure (Charles’s law)
$
\mathbf{V} \propto \mathbf{T}
$
- As the temperature of the gas increases, its volume increases and vice versa
- A gas thermometer must be calibrated – by knowing the temperature of the gas at a certain volume, a temperature scale can be determined depending on how quickly the gas expands with temperature
Resistance of a Metal
- Recall that electrical resistance changes with temperature e.g. the resistance of a filament lamp increases when current increases through it
- For metals: resistance increases with temperature at a steady rate
- For thermistors: resistance changes rapidly over a narrow range of temperatures
- As a thermistor gets hotter, its resistance decreases
- This means a thermometer based on a thermistor can be used to measure a range of temperatures
- The relationship between the resistance and temperature is non-linear
- This means the graph of temperature against resistance will be a curved line and the thermistor will have to be calibrated
E.M.F. of a Thermocouple
- A thermocouple is an electrical device used as the sensor of a thermometer
- It consists of two wires of different, or dissimilar, metals attached to each other, producing a junction on one end
- The opposite ends are connected to a voltmeter
- When this junction is heated, an e.m.f. is produced between the two wires which is measured on the voltmeter
- The greater the difference in temperature between the wires, the greater the e.m.f
- However, a thermocouple requires calibration since the e.m.f. does not vary linearly with temperature
- The graph against e.m.f. and temperature is a positive, curved line
Exam Tip
Remember to relate how the temperature is measured for different types of thermometer back to the scenario in the question. For example, make sure you say: the temperature increases as the volume of gas increases or the temperature increases as the e.m.f. between the two wires increases.
14.1.4 THE KELVIN SCALE
Scale of Thermodynamic Temperature
- As an everyday scale of temperature, Celsius $\left({ }^{\circ} \mathrm{C}\right)$ is the most familiar
- This scale is based on the properties of water – the freezing point of water was taken as taken as $0^{\circ} \mathrm{C}$ and the boiling point as $100^{\circ} \mathrm{C}$
- However, there is nothing special about these two temperatures
- The freezing and boiling point of water will actually change as its pressure changes
- The Celsius scale is used to measure the temperature in a liquid-in-glass thermometer
- However, the expansion of the liquid might be non-linear
- Other temperature scales include:
- Fahrenheit, commonly used in the US
- Kelvin, used in thermodynamics
- The Kelvin scale is known as the thermodynamic scale and was designed to overcome the problem with scales of temperature
- The thermodynamic scale is said to be an absolute scale that is not defined in terms of a property of any particular substance
- This is because thermodynamic temperatures do not depend on the property of any particular substance
Absolute Zero
- On the thermodynamic (Kelvin) temperature scale, absolute zero is defined as:
The lowest temperature possible. Equal to $0 \mathrm{~K}$ or $-273.15{ }^{\circ} \mathrm{C}$ - It is not possible to have a temperature lower than $0 \mathrm{~K}$
- This means a temperature in Kelvin will never be a negative value
- Absolute zero is defined in kinetic terms as:
The temperature at which the atoms and molecules in all substances have zero kinetic and potential energy - This means for a system at $0 \mathrm{~K}$, it is not possible to remove any more energy from it
- Even in space, the temperature is roughly $2.7 \mathrm{~K}$, just above absolute zero
Using the Kelvin Scale
- To convert between temperatures $\theta$ in the Celsius scale, and $T$ in the Kelvin scale, use the following conversion:
$
\begin{aligned}
& \theta /{ }^{\circ} \mathrm{C}=T / K-273.15 \\
& T / K=\theta /{ }^{\circ} \mathrm{C}+273.15
\end{aligned}
$
- The divisions on both scales are equal. This means:
A change in a temperature of $1 \mathrm{~K}$ is equal to a change in temperature of $1^{\circ} \mathrm{C}$
Worked example: Kelvin conversion
In many ideal gas problems, room temperature is considered to be $300 \mathrm{~K}$. What is this temperature in Celsius?
Answer/Explanation
Step 1:
Kelvin to Celsius equation
$
\theta /{ }^{\circ} \mathrm{C}=\mathrm{T} / \mathrm{K}-273.15
$
Step 2:
Substitute in value of $300 \mathrm{~K}$
$
300 \mathrm{~K}-273.15=26.85^{\circ} \mathrm{C}
$
Exam Tip
If you forget in the exam whether it’s +273.15 or -273.15 , just remember that $0{ }^{\circ} \mathrm{C}=273.15 \mathrm{~K}$. This way, when you know that you need to +273.15 to a temperature in degrees to get a temperature in Kelvin. For example: $0{ }^{\circ} \mathrm{C}+$ $273.15=273.15 \mathrm{~K}$.