Heat and Thermodynamics: Structured Study Notes for PHY 103

Temperature, Heat, and Thermodynamic Laws

Key Concepts in Heat and Thermodynamics

Heat and thermodynamics are foundational topics in physics, describing energy transfer, temperature, and the behavior of matter. Understanding these concepts is essential for analyzing physical systems and their energy exchanges.

• Temperature: A measure of the average kinetic energy of particles in a substance.

• Heat: Energy transferred between objects due to a temperature difference.

• Thermal Contact: When two objects can exchange energy.

• Thermal Equilibrium: When two objects in contact no longer exchange energy.

• Zeroth Law of Thermodynamics: If two objects are each in thermal equilibrium with a third, they are in equilibrium with each other.

Temperature Scales and Thermometers

Temperature can be measured using various scales and devices, each based on physical properties that change with temperature.

• Kelvin (Thermodynamic) Scale: Absolute scale; ice point at 273.15 K, triple point at 273.16 K, steam point at 373.15 K.

• Celsius Scale: Ice point at 0°C, steam point at 100°C, divided into 100 intervals.

• Fahrenheit Scale: Ice point at 32°F, steam point at 212°F, divided into 180 intervals.

• Thermometers: Devices that measure temperature using thermometric properties (e.g., liquid expansion, gas pressure, electrical resistance).

Conversion Formulas:

• $T_K = T_C + 273.15$

• $T_F = \frac{9}{5} T_C + 32$

• $T_C = \frac{5}{9}(T_F - 32)$

Defining a Temperature Scale: Choose a substance, select a thermometric property, measure at two fixed points, and assign values using:

• $T_m = \frac{X_m - X_L}{X_U - X_L} N + T_L$

Thermal Expansion of Solids and Liquids

Thermal Expansion Principles

When temperature increases, most solids and liquids expand due to increased atomic separation. This phenomenon is crucial in engineering and construction.

• Linear Expansion: $\Delta L = \alpha L_i \Delta T$

• Volume Expansion: $\Delta V = \gamma V_i \Delta T$

• Area Expansion: $\Delta A = \beta A_i \Delta T$

• For solids: $\gamma = 3\alpha$, $\beta = 2\alpha$

Example: Expansion joints in bridges and railways accommodate thermal expansion.

Heat Capacity, Specific Heat, and Latent Heat

Heat Capacity and Specific Heat

Heat capacity ($C$) is the energy needed to raise the temperature of a sample by 1°C. Specific heat ($c$) is the energy needed to raise 1 kg of a substance by 1°C.

• $C = \frac{Q}{\Delta T}$

• $c = \frac{Q}{m \Delta T}$

• $Q = m c \Delta T$

Latent Heat

Latent heat ($L$) is the energy required for a phase change without temperature change.

• $Q = m L$

• Types: Latent heat of fusion (melting), vaporization (boiling), sublimation (solid to gas).

Ideal Gas Law and Kinetic Theory

Macroscopic Description of an Ideal Gas

An ideal gas follows the equation of state, relating pressure, volume, and temperature:

• $PV = nRT$

• $PV = N k_B T$

Kinetic Theory of Gases

The kinetic theory explains gas pressure as a result of molecular collisions. Assumptions include large numbers of molecules, random motion, elastic collisions, and negligible intermolecular forces except during collisions.

• Pressure is proportional to the number of molecules per unit volume and their average kinetic energy.

• Average kinetic energy per molecule: $\frac{3}{2} k_B T$

• Degrees of freedom: Monoatomic (3), Diatomic (5), Polyatomic (6)

First Law of Thermodynamics

Energy Conservation in Thermodynamic Systems

The first law states that the change in internal energy ($\Delta E_{int}$) of a system is equal to the heat added ($Q$) minus the work done ($W$):

• $\Delta E_{int} = Q - W$

• Positive $Q$: energy enters system; positive $W$: work done by system.

Special Thermodynamic Processes

• Isolated System: No heat or work exchange; internal energy constant.

• Cyclic Process: Returns to initial state; internal energy change is zero.

• Isobaric Process: Constant pressure; $W = P (V_f - V_i)$

• Isochoric Process: Constant volume; $W = 0$, $\Delta E_{int} = Q$

• Isothermal Process: Constant temperature; $\Delta E_{int} = 0$, $Q = W$

Second Law of Thermodynamics and Heat Engines

Heat Engines and Efficiency

A heat engine converts heat energy into work, operating between a hot and cold reservoir. Efficiency ($e$) is the ratio of work output to heat input:

• $e = \frac{W}{|Q_h|} = 1 - \frac{|Q_c|}{|Q_h|}$

The second law states that no engine can convert all heat into work; some energy is always expelled to the cold reservoir.

Heat Pumps and Refrigerators

These devices transfer heat from cold to hot reservoirs, requiring work input. Their performance is measured by the coefficient of performance (CoP):

• Cooling mode: $CoP = \frac{|Q_c|}{W}$

• Heating mode: $CoP = \frac{|Q_h|}{W}$

Carnot Engine and Maximum Efficiency

The Carnot engine is an ideal, reversible heat engine. Its efficiency depends only on the temperatures of the reservoirs:

• $e_{Carnot} = 1 - \frac{T_c}{T_h}$

Maximum efficiency is achieved only if the cold reservoir is at absolute zero, which is impossible in practice.

Third Law of Thermodynamics

Absolute Zero and Entropy

The third law states that the entropy of a perfect crystal at absolute zero is zero. Absolute zero (0 K) is unattainable experimentally, and at this temperature, all molecular motion ceases.

• Entropy formula: $S = k_B \ln \Omega$

Energy Transfer Mechanisms

Conduction

Heat transfer by conduction occurs as molecules in a hot region transfer energy to adjacent cooler regions. The rate of energy transfer is given by:

• $P = \frac{Q}{\Delta t} = kA \frac{T_h - T_c}{\Delta x}$

• Thermal resistance: $R = \frac{\Delta x}{kA}$

Convection

Convection occurs as heated fluid rises due to decreased density, transferring energy throughout the fluid.

Radiation

All objects emit energy as electromagnetic waves. The rate of energy emission is given by Stefan-Boltzmann law:

• $P_{rad} = \sigma \epsilon A T^4$

• $P_{net} = \sigma \epsilon A (T^4 - T_{env}^4)$

Summary Table: Temperature Scales

Scale	Ice Point	Steam Point	Interval	Conversion
Kelvin	273.15 K	373.15 K	100	$T_K = T_C + 273.15$
Celsius	0°C	100°C	100	$T_C = T_K - 273.15$
Fahrenheit	32°F	212°F	180	$T_F = \frac{9}{5} T_C + 32$

Summary Table: Types of Thermometers

Type	Thermometric Property	Range
Liquid-in-glass	Length of liquid column	-35°C to 350°C (mercury)
Gas (constant volume)	Pressure	-270°C to 1500°C
Resistance	Electrical resistance	-200°C to 1000°C (platinum)
Thermocouple	EMF	-270°C to 2000°C

Summary Table: Energy Transfer Mechanisms

Mechanism	Description	Formula
Conduction	Direct transfer via collisions	$P = kA \frac{T_h - T_c}{\Delta x}$
Convection	Bulk movement of fluid	--
Radiation	Electromagnetic emission	$P_{rad} = \sigma \epsilon A T^4$