Chapter 13: Fluids and Phases of Matter

Phases of Matter

The phases of matter describe the distinct forms that different phases of matter take on. The most common phases are solid, liquid, and gas.

• Solid: Has a fixed shape and volume; particles are closely packed and vibrate in place.

• Liquid: Has a fixed volume but takes the shape of its container; particles are less tightly packed and can move past one another.

• Gas: Has neither fixed shape nor volume; particles are far apart and move freely.

• Plasma: Ionized gas with free electrons, found in stars and lightning (additional info).

• Phase transitions: Changes between phases (e.g., melting, freezing, evaporation).

Density and Specific Gravity

Density is a measure of mass per unit volume, while specific gravity compares the density of a substance to that of water.

• Density (): , where is mass and is volume.

• Specific Gravity: (dimensionless).

• Example: If a metal has a density of , its specific gravity is .

Pascal’s Principle

Pascal’s Principle states that a change in pressure applied to an enclosed fluid is transmitted undiminished to all portions of the fluid and to the walls of its container.

• Formula: , where is pressure, is force, and is area.

• Application: Hydraulic lifts use Pascal’s Principle to multiply force.

Buoyancy and Archimedes’ Principle

Buoyancy is the upward force exerted by a fluid on an object placed in it. Archimedes’ Principle states that the buoyant force is equal to the weight of the fluid displaced by the object.

• Buoyant Force ():

• Archimedes’ Principle: Explains why objects float or sink.

• Example: A boat floats because it displaces a volume of water whose weight equals the boat’s weight.

Bernoulli’s Equation

Bernoulli’s Equation relates the pressure, velocity, and height in a moving fluid, assuming the fluid is incompressible and non-viscous.

• Equation:

• Application: Used to analyze fluid flow in pipes, such as water circulation in a house.

• Example Problem: Given two pipe diameters and heights, use Bernoulli’s Equation and the continuity equation () to solve for unknown pressure and velocity.

Chapter 17: Temperature, Thermal Expansion, and Gas Laws

Temperature and Thermometers

Temperature measures the average kinetic energy of particles in a substance. Thermometers are devices used to measure temperature.

• Temperature Scales: Celsius (°C), Fahrenheit (°F), Kelvin (K).

• Conversions:

• Example: Room temperature (68°F) in Celsius:

Thermal Expansion

Thermal expansion is the increase in size of an object as its temperature increases.

• Linear Expansion:

• Table 17-1: Contains coefficients of linear expansion for various materials (additional info).

• Example: Metal rails expand in summer heat, requiring expansion joints.

The Gas Laws and Absolute Temperature

Gas laws describe the behavior of gases in terms of pressure, volume, and temperature.

• Boyle’s Law: (at constant temperature)

• Charles’s Law: (at constant pressure)

• Absolute Temperature: Measured in Kelvin, the zero point is absolute zero.

The Ideal Gas Law

The Ideal Gas Law relates pressure, volume, temperature, and number of moles of a gas.

• Equation:

• Variables: = pressure, = volume, = moles, = gas constant (), = temperature in Kelvin.

• Example: Calculate the volume of 1 mole of gas at given pressure and temperature.

Ideal Gas Law in Terms of Molecules: Avogadro’s Number

Avogadro’s Number () is the number of molecules in one mole of a substance.

• Value:

• Molecular Form: , where is number of molecules, is Boltzmann’s constant ().

• Example: Calculate molecules per at STP using .

Chapter 18: Real Gases, Phase Changes, and Humidity

Real Gases and Changes of Phase

Real gases deviate from ideal behavior at high pressures and low temperatures. Phase changes include melting, freezing, vaporization, condensation, and sublimation.

• Phase Diagrams: Graphs showing regions of solid, liquid, and gas phases (additional info).

• Critical Point: The temperature and pressure above which a gas cannot be liquefied.

Vapor Pressure and Humidity

Vapor pressure is the pressure exerted by a vapor in equilibrium with its liquid. Humidity refers to the amount of water vapor in the air.

• Condensation: Gas to liquid phase change.

• Evaporation: Liquid to gas phase change.

• Partial Pressure: The pressure contributed by a single component in a mixture of gases.

• Relative Humidity:

Chapter 19: Heat, Calorimetry, and Thermodynamics

Heat as Energy Transfer

Heat is the transfer of energy due to temperature difference.

• Unit: Joule (J) or calorie (cal).

• Direction: Heat flows from hot to cold objects.

Calorimetry

Calorimetry is the measurement of heat transfer in physical and chemical processes.

• Equation: , where is heat, is mass, is specific heat, is temperature change.

• Example: Mixing ice and water to find final temperature.

Latent Heat

Latent heat is the energy absorbed or released during a phase change at constant temperature.

• Fusion: Solid to liquid ()

• Vaporization: Liquid to gas ()

• Equation: , where is latent heat.

• Example Problem: Calculate mass of ice cube using heat transfer equations.

The First Law of Thermodynamics

The First Law of Thermodynamics states that energy cannot be created or destroyed, only transferred or transformed.

• Equation: , where is change in internal energy, is heat added, is work done by the system.

• Sign Conventions: Positive means heat added; positive means work done by the system.

Heat Transfer: Conduction, Convection, Radiation

Heat can be transferred by three mechanisms:

• Conduction: Transfer through direct contact;

• Convection: Transfer by movement of fluid.

• Radiation: Transfer by electromagnetic waves;

Chapter 20: Second Law of Thermodynamics and Heat Engines

Reversible and Irreversible Processes; Carnot Engine

Reversible processes can be reversed without net energy change; irreversible processes cannot. The Carnot engine is an idealized heat engine with maximum possible efficiency.

• Carnot Cycle: Consists of two isothermal and two adiabatic processes.

• Maximum Efficiency: , where and are cold and hot reservoir temperatures in Kelvin.

• Example: For , , or 23%.

Formula Sheet Tips

• Include all relevant formulas from the textbook.

• Ensure correct units and input values (e.g., use Kelvin for temperature, absolute pressure).

Sample Table: Coefficients of Linear Expansion (Inferred from Table 17-1)