LU1 - TEMPERATURE

Temperature

  • Temperature is an SI base quantity related to hot and cold and measured in Kelvins (K).

  • Absolute zero, the lowest limit of temperature, is 0 K.

  • Room temperature is approximately 290 K.

  • The universe's average temperature is about 3 K, but it was around 10^{9} K at its beginning 13.7 billion years ago.

Zeroth Law of Thermodynamics

  • Defines temperature as a valid concept and is fundamental to the first and second laws of thermodynamics.

  • If bodies A and B are each in thermal equilibrium with a third body T, then A and B are in thermal equilibrium with each other.

  • When two bodies are in thermal equilibrium, their temperatures are equal, and vice versa.

Measuring Temperature

  • Kelvin scale is used for temperature measurements.

  • A standard fixed point is selected, and a temperature is assigned to its environment.

Triple Point of Water

  • The triple point of water is the chosen reproducible thermal phenomenon for setting up a temperature scale.

  • It is the unique condition where liquid water, solid ice, and water vapor can coexist in thermal equilibrium.

  • Assigned a standard fixed-point temperature of 273.16 K.

Constant-Volume Gas Thermometer

  • A gas-filled bulb connected to a mercury manometer used to measure temperature.

  • Volume is kept constant by adjusting reservoir R.

  • Temperature is defined as T = Cp, where p is the pressure of the gas and C is a constant.

  • Pressure p in the thermometer is given by p = p0 - \rho g h, where p0 is the atmospheric pressure, \rho the density of mercury, and h the height difference in the manometer.

  • Temperature is calculated using the formula T = (273.16 K) \frac{p}{p3}, where p3 is the pressure at the triple point.

  • To obtain accurate measurements, the amount of gas in the bulb is reduced to extrapolate the ratio \frac{p}{p3} as gas approaches zero: T = (273.16 K) \lim{gas \to 0} \frac{p}{p_3}.

Celsius and Fahrenheit Scales

  • Celsius scale is commonly used with the unit degrees Celsius (°C).

  • The Celsius degree has the same magnitude as the Kelvin.

  • T_C = T - 273.15^\circ where T is in Kelvins.

  • Fahrenheit scale is used in the United States.

  • TF = \frac{9}{5}TC + 32^\circ

Key Temperatures

  • Boiling point of water: 100 °C, 212 °F

  • Freezing point of water: 0 °C, 32 °F

  • Scales coincide at -40 °C = -40 °F

Thermal Expansion

  • Objects change size with temperature changes.

Linear Expansion

  • The change in length \Delta L of a material with initial length L is related to the temperature change \Delta T by \Delta L = L \alpha \Delta T, where \alpha is the coefficient of linear expansion.

Volume Expansion

  • The change in volume \Delta V of a solid or liquid with initial volume V is related to the temperature change \Delta T by \Delta V = V \beta \Delta T,

  • \beta is the coefficient of volume expansion.

  • For solids, \beta = 3 \alpha