Temperature and temperature scales Knowledge-Based Study

Study notes

1. What is Temperature?

   Temperature is a macroscopic measure of the average translational kinetic energy of the constituent particles of a substance. It determines the direction of net heat flow between two bodies placed in thermal contact: thermal energy naturally flows from a body at a higher temperature to one at a lower temperature until both reach thermal equilibrium.

   The foundational principle governing temperature measurement is the Zeroth Law of Thermodynamics. It states that if body A is in thermal equilibrium with body B, and body B is in thermal equilibrium with body C, then body A is also in thermal equilibrium with body C. This allows us to use body B as a thermometer to define and measure the temperature of any system consistently.

   Measuring Temperature

   A thermometer relies on a physical property that changes reproducibly with temperature, known as a thermometric property. Examples include:

   • Volume expansion of a liquid column (e.g., mercury or alcohol thermometers)
   • Pressure change of a gas at constant volume (constant-volume gas thermometer)
   • Electrical resistance of a metal conductor (e.g., platinum resistance thermometer)
   • Electromotive force across a junction of dissimilar metals (thermocouple)

   To establish a scale, two fixed reproducible points are traditionally chosen: the lower fixed point (the melting point of pure ice at 1 atm) and the upper fixed point (the boiling point of pure water at 1 atm). The interval between these two reference points is then divided into equal intervals or degrees.

   Comparing Common Scales

   Three principal temperature scales are widely used in physics and everyday applications:

   • Celsius scale (°C): Assigns 0 °C to the ice point and 100 °C to the steam point, with 100 equal divisions between them.
   • Fahrenheit scale (°F): Assigns 32 °F to the ice point and 212 °F to the steam point, resulting in 180 equal divisions between the fixed points.
   • Kelvin scale (K): The SI base unit of thermodynamic temperature. It sets absolute zero as 0 K and assigns 273.16 K to the triple point of water. The size of one kelvin is identical to the size of one degree Celsius.

   The mathematical relationships connecting these scales are:

   $$T_{\text{F}} = \frac{9}{5}T_{\text{C}} + 32$$

   $$T = T_{\text{C}} + 273.15$$

   where $T$ is temperature in kelvins, $T_{\text{C}}$ is in degrees Celsius, and $T_{\text{F}}$ is in degrees Fahrenheit.

   The Significance of Absolute Zero

   When constant-volume gas thermometers filled with different low-density gases are calibrated, plotting pressure $P$ against temperature in Celsius reveals a common extrapolation point. Regardless of the gas used, extrapolating the pressure-temperature line to zero pressure indicates an intercept at approximately $-273.15\text{ }^\circ\text{C}$.

   This theoretical point is defined as absolute zero (0 K). At absolute zero, the classical kinetic energy of translational motion ceases, and a system possesses its minimum possible energy (zero-point energy in quantum mechanics). Because temperature on the Kelvin scale is directly proportional to internal energy in ideal gases, the Kelvin scale is an absolute scale and does not take negative values.