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 $p = p<em>0 - \rho g h$, where $p</em>0$ is the atmospheric pressure, $\rho$ the density of mercury, and $h$ the height difference in the manometer.

• Temperature is calculated using the formula $T = (273.16 K) \frac{p}{p<em>3}$, where $p</em>3$ is the pressure at the triple point.

• To obtain accurate measurements, the amount of gas in the bulb is reduced to extrapolate the ratio $\frac{p}{p<em>3}$ as gas approaches zero: $T = (273.16 K) \lim</em>{gas \to 0} \frac{p}{p_3}$.

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.

• $T<em>F = \frac{9}{5}T</em>C + 32^\circ$

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, $\beta = 3 \alpha$