CIE AS & A Level Physics 9702: Topic 14: Temperature- Unit : 14.2 Temperature scales Study Notes

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: $0{ }^{\circ} \mathrm{C}+$ $273.15=273.15 \mathrm{~K}$.

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