Fundamental Concepts in Thermodynamics and Gas Behavior

Shock Waves: Formation and Mach Cone Angle

If the speed of a source relative to the medium exceeds the speed of sound in the medium, the Doppler equation no longer applies. In such a case, shock waves result. The half-angle of the Mach cone is given by:

Temperature Measurement and Thermometers

Temperature is an SI base quantity related to our sense of hot and cold. It is measured with a thermometer, which contains a working substance with a measurable property, such as length or pressure, that changes in a regular way as the substance becomes hotter or colder.

Zeroth Law of Thermodynamics: Thermal Equilibrium

When a thermometer and some other object are placed in contact with each other, they eventually reach thermal equilibrium. The reading of the thermometer is then taken to be the temperature of the object. This process provides consistent and useful temperature measurements because of the Zeroth Law of Thermodynamics: "If bodies A and B are each in thermal equilibrium with a third body C, then A and B are in thermal equilibrium with each other."

First Law of Thermodynamics: Energy Conservation

The principle of conservation of energy for a thermodynamic process is expressed in the First Law of Thermodynamics, which may assume either of the forms. Here, U represents the internal energy of the material, which depends only on the material's state. Q represents the energy exchanged as heat between the system and its surroundings. Q is positive if the system absorbs heat and negative if the system loses heat. W is the work done by the system.

Applications of the First Law: Adiabatic Processes

For adiabatic processes, Q = 0. Other applications include: W = 0, Q = W = ...

Second Law of Thermodynamics: Entropy and Processes

This law, which is an extension of the entropy postulate, states: "If a process occurs in a closed system, the entropy of the system increases for irreversible processes and remains constant for reversible processes. It never decreases." In equation form:

The Kelvin Temperature Scale: SI Standard

In the SI system, temperature is measured on the Kelvin scale, which is based on the triple point of water (273.16 K).

Kinetic Theory of Gases: Macroscopic to Microscopic

The Kinetic Theory of Gases relates the macroscopic properties of gases (such as pressure and temperature) to the microscopic properties of gas molecules (such as speed and kinetic energy).

Avogadro's Number: Moles and Elementary Units

One mole of a substance contains N_A elementary units, where N_A (Avogadro's Number) is found experimentally to be approximately 6.022 x 10²³ mol^-1.

Ideal Gas Law: Pressure, Volume, and Temperature

An ideal gas is one for which the pressure p, volume V, and temperature T are related by the Ideal Gas Law: pV = nRT.

Work in Isothermal Volume Change for Ideal Gases

The work done by an ideal gas during an isothermal (constant-temperature) change from volume V_i to V_f is given by:

Pressure, Temperature, and Molecular Speed in Gases

The pressure exerted by n moles of an ideal gas, in terms of the speed of its molecules, is: