Thermodynamics: Temperature, Thermal Expansion, and Heat- lecture 27

Thermodynamics

Temperature

Temperature is a measure of the average molecular kinetic energy (internal energy) of a material. It is a fundamental concept in thermodynamics and is used to quantify how hot or cold an object is. The most common temperature scales are Celsius, Fahrenheit, and Kelvin.

• Celsius (°C): Widely used in science, with 0°C as the freezing point and 100°C as the boiling point of water at 1 atm pressure.

• Fahrenheit (°F): Common in the United States, with 32°F as the freezing point and 212°F as the boiling point of water.

• Kelvin (K): The SI unit for temperature, starting at absolute zero (the lowest possible temperature). 0 K = -273.15°C.

Temperature Conversion Formulas:

• From Fahrenheit to Celsius: $T_C = \frac{5}{9}(T_F - 32)$

• From Celsius to Fahrenheit: $T_F = \frac{9}{5}T_C + 32$

• From Celsius to Kelvin: $T_K = T_C + 273.15$

Key Points:

• Temperature changes are measured in degrees Celsius (°C), Fahrenheit (°F), or kelvin (K).

• 1 K change is equivalent to a 1°C change.

• Kelvin does not use the term "degree"; it is simply "kelvin" (K).

Thermal Expansion

Thermal expansion is the tendency of matter to change its shape, area, and volume in response to a change in temperature. This occurs because particles move more and occupy more space as temperature increases.

• Linear Thermal Expansion: The change in length ($\Delta L$) of an object is proportional to its original length ($L_0$) and the change in temperature ($\Delta T$):

$\Delta L = \alpha L_0 \Delta T$

• $\alpha$ is the linear thermal expansion coefficient (unit: $\mathrm{C}^{-1}$).

• Volume Thermal Expansion: The change in volume ($\Delta V$) is given by:

$\Delta V = \beta V_0 \Delta T$

• $\beta$ is the volume thermal expansion coefficient (unit: $\mathrm{C}^{-1}$).

• For most solids, $\beta \approx 3\alpha$.

Different materials expand at different rates, characterized by their expansion coefficients.

Example: When a metal lid is stuck on a glass jar, running hot water over the lid causes it to expand more than the glass, making it easier to open.

Heat

Heat is the energy that flows from a hotter object to a colder one due to a temperature difference. The SI unit of heat is the joule (J). Another common unit is the calorie (cal), where 1 cal = 4.186 J. In nutrition, the Calorie (Cal) is used, which is equal to 1000 cal or 4186 J.

• Heat transfer continues until thermal equilibrium is reached (no temperature difference).

• Heat can cause a change in temperature or a change in phase (state) of a substance.

Heat and Temperature Change

The amount of heat ($Q$) required to change the temperature of a mass ($m$) of a substance with specific heat capacity ($c$) by $\Delta T$ is:

$Q = c m \Delta T$

• Specific heat capacity (c): The amount of heat needed to raise the temperature of 1 kg of a substance by 1°C (unit: $\mathrm{J}/(\mathrm{kg} \cdot \mathrm{C})$).

Heat and Phase Change

When a substance undergoes a phase change (e.g., melting, boiling), the temperature remains constant until the phase change is complete. The heat required for a phase change is called latent heat ($L$):

$Q_{\text{phase}} = m L_{\text{phase}}$

• Latent heat of fusion ($L_F$): For melting/freezing.

• Latent heat of vaporization ($L_V$): For boiling/condensing.

• Latent heat of sublimation ($L_S$): For sublimation/deposition.

Example: The total heat to raise a substance from below its boiling point to above its boiling point:

$Q = Q_1 + Q_V + Q_2 = m c_1 \Delta T_1 + m L_V + m c_2 \Delta T_2$

Key Points:

• During a phase change, temperature does not change until the phase transition is complete.

• Latent heat is measured in $\mathrm{J}/\mathrm{kg}$.