Matter and Heat - The Physical Universe

The Physical Universe - Matter and Heat

Chapter 5 Outline: Main Ideas

• Temperature and Heat

  • Defining temperature

  • Changing temperature: heat

• Understanding Fluids

  • Density, pressure, buoyancy

  • Gas laws

• Kinetic Theory of Gases

  • Motion and temperature

  • Heat transfer

• Changes of States

  • Liquids and solids

  • Evaporation and boiling

• Transformation of Energy

  • Entropy and the fate of the universe

Temperature

• Conceptual Understanding: How "hot" or "cold" something is.

• Scientific Definition: The temperature of a substance is proportional to the average kinetic energy per molecule of the molecules that make up the substance.

• Measurement: Temperature is usually measured with thermometers.

• Temperature Scales:

  • Celsius:

    • Water freezes at $0^{\circ}\text{C}$.

    • Water boils at $100^{\circ}\text{C}$.

  • Fahrenheit:

    • Water freezes at $32^{\circ}\text{F}$.

    • Water boils at $212^{\circ}\text{F}$.

  • Celsius and Fahrenheit scales are based on the properties of water.

  • Kelvin (Absolute) Scale:

    • Water freezes at $273 \text{ K}$.

    • $0 \text{ K}$ is "Absolute zero"; at this point, particles have minimum kinetic energy.

    • The Kelvin scale is not dependent upon any particular material.

• Importance of the Absolute Scale:

  • Temperature relates to average kinetic energy.

  • Celsius and Fahrenheit use negative values, which implies "negative energy"—a concept that does not make sense physically.

  • The Kelvin scale avoids negative values, accurately reflecting that kinetic energy cannot be negative.

• Thermal Expansion:

  • The property of a material to increase in volume with increasing temperature.

  • Application: Bimetallic strips, used in devices like thermocouple switches for furnaces or air conditioners.

    • A bimetallic strip consists of two different metals (Metal A and Metal B) bonded together.

    • These metals expand at different rates when heated, causing the strip to bend and activate a switch.

Heat

• Definition: Heat is the sum of the kinetic energies of all the separate particles that make up a body.

  • More heat means more internal energy.

  • Heat is a form of energy.

• Unit: The SI unit of heat is the Joule ($\text{J}$).

• Internal Energy: The total amount of kinetic and potential energy possessed by a body.

  • Internal energy can be changed by the transfer of heat.

• Direction of Heat Transfer:

  • Heat is always transferred FROM a body of HIGH TEMPERATURE TO a body of LOW TEMPERATURE.

  • This transfer alters the internal energy of the bodies involved.

Specific Heat Capacity

• Concept: Different materials alter their internal energy at different "rates"; they have different capacities for storing internal energy.

• Formal Definition: The quantity of heat required to change the temperature of a unit mass of a substance by $\text{1}^{\circ}\text{C}$.

• Conceptual Analogy: Think of specific heat like "thermal inertia" or "resistance" of a material to changes in its temperature.

  • An object whose temperature is easily changed has LOW thermal inertia and LOW specific heat capacity (e.g., butter).

  • An object whose temperature is difficult to change has LARGE thermal inertia and LARGE specific heat capacity (e.g., water).

Heat Transfer Processes

• Heat always travels FROM HOT TO COLD.

• There are three main ways to transfer heat:

  1. Conduction (primarily in solids)

     • Defined as heat transfer due to molecular collisions.

     • Different material properties imply different "thermal conductivity," dependent on the bonding of atoms/molecules.

     • Good Thermal Conductors: Materials with many "extra" electrons, like metals (gold, silver, copper).

     • Gases are poor conductors because molecules are far apart, leading to infrequent collisions.

     • Thermal Insulator: A material that is a poor thermal conductor (e.g., wood, cork, air, snow, Styrofoam).

  2. Convection (primarily in fluids - liquids and gases)

     • Heat is transferred by the actual motion of the substance itself.

     • Most important in the atmosphere: warm air rises, creating "convection currents" that stir the atmosphere and influence climate/weather.

  3. Radiation (all objects emit and absorb)

     • Heat transfer in the form of electromagnetic waves.

     • The Sun is a primary example of heat transfer via radiation.

     • All objects continuously radiate and absorb energy.

     • Effect: If more energy is absorbed than given off, temperature ($\text{T}$) goes up; if more energy is given off than absorbed, $T$ goes down.

     • Good Absorbers: Dark surfaces, pupils of eyes.

Understanding Fluids

Density

• Definition: Mass divided by Volume.

  • $\text{Density} = \frac{\text{Mass}}{\text{Volume}}$

• Takes into account both the mass of the atoms and the distance between atoms.

• SI Unit: $\text{kg/m}^3$.

• Symbol: Often denoted by the Greek letter "rho" ($\rho$).

• Density of water: $1000 \text{ kg/m}^3$ or $1 \text{ g/cm}^3$.

Characterizing States of Matter

• Liquids:

  • Atoms are not "fixed"; they can move around.

  • Liquids take the shape of the container that holds them.

• Gases:

  • Properties similar to liquids but with even greater freedom of motion for atoms/molecules.

  • Still flow and take the shape of their container.

  • Distance between atoms/molecules is generally greater than in liquids (at normal pressures).

Pressure

• Definition: Force exerted perpendicular per unit area.

• SI Unit: Newton per square meter ($\text{N/m}^2$).

  • This unit has a special name: Pascal ($\text{Pa}$).

  • $1 \text{ Pa} = 1 \text{ N/m}^2$.

  • A pascal is a very small unit; the pressure exerted by a $1$ dollar bill laying flat on a table is roughly $1 \text{ Pa}$.

  • More commonly, you'll hear kilo-Pascal (kPa) ($1 \text{ kPa} = 1000 \text{ Pa}$).

    • Example: Atmospheric pressure is approximately $100 \text{ kPa}$ at sea level.

• Force vs. Pressure: They are related but not equivalent.

  • Example: A small woman ($50 \text{ kg}$) in high heels ($1 \text{ cm}^2$ per heel) vs. a delivery guy ($100 \text{ kg}$) in large boots ($100 \text{ cm}^2$ per heel).

    • Woman's force (weight) $= 500 \text{ N}$; Pressure $= \frac{500 \text{ N}}{0.0002 \text{ m}^2} = 2,500,000 \text{ N/m}^2$.

    • Delivery guy's force (weight) $= 1000 \text{ N}$; Pressure $= \frac{1000 \text{ N}}{0.02 \text{ m}^2} = 50,000 \text{ N/m}^2$.

    • The woman exerts significantly more pressure due to the smaller area.

• Pressure in a Fluid:

  • Forces exerted by the fluid act perpendicular to boundary walls.

  • At a given depth, pressure is the same in all directions.

  • Any external pressure exerted on a fluid is transmitted uniformly throughout the fluid.

• Pressure at Depth in an Open Liquid Container:

  • Pressure ($P$) depends on the distance below the surface.

  • $P = \rho \text{gd}$

    • Where $\rho$ (rho) = mass density of the liquid

    • $\text{g}$ = acceleration due to gravity ($\approx 10 \text{ m/s}^2$)

    • $\text{d}$ = depth = distance below the surface

Buoyancy

• Concept: Because pressure depends on depth, there is a net upward pressure on any object immersed in a liquid.

• Buoyant Force ($F_b$):

  • If $F_b$ on an immersed object is equal to or greater than its weight, the object floats.

  • If $F_b$ is less than its weight, the object sinks.

• Archimedes' Principle:

  • An immersed body experiences an upward force (buoyant force) equal to the weight of the fluid displaced by the body.

  • Important: The buoyant force does not depend on the weight of the object itself; it only depends on the weight of the displaced fluid.

  • Weight Force: $\text{W}<em>{object} = \text{mass}</em>{object} \times \text{g} = \rho<em>{object} \times \text{V}</em>{object} \times \text{g}$

  • Buoyant Force: $F<em>b = \text{mass}</em>{displaced_water} \times \text{g} = \rho<em>{water} \times \text{V}</em>{displaced} \times \text{g}$

• Condition for Floating:

  • For an object to float, $F<em>b = \text{W}</em>{object}$.

  • Therefore, $\rho<em>{water} \times \text{V}</em>{displaced} \times \text{g} = \rho<em>{object} \times \text{V}</em>{object} \times \text{g}$.

  • This simplifies to: $\rho<em>{water} \times \text{V}</em>{displaced} = \rho<em>{object} \times \text{V}</em>{object}$.

• Discussion Example: Two blocks ($1 \text{ cm}^3$ each); Lead ($\rho = 11,300 \text{ kg/m}^3$) and Wood ($\rho = 800 \text{ kg/m}^3$).

  • Lead block has greater mass ($\text{Mass} = \rho \times \text{V}$).

  • If both are completely submerged (displacing the same volume of water), the buoyant force is the same on both, because $F<em>b$ depends only on the weight of the displaced fluid ($\rho</em>{water} \times \text{V}_{displaced} \times \text{g}$) and not the object's weight.

  • If the wooden block floats with $1/5$ out of water, it displaces less water than the fully submerged lead block, so the buoyant force on the lead block is greater in this scenario.

Gas Laws

• These laws describe the relationships among the pressure ($P$), temperature ($T$), and volume ($V$) of a gas.

• Boyle's Law (Constant Temperature):

  • If a gas is held at constant temperature, the initial pressure ($P<em>i$) and volume ($V</em>i$) are related to final pressure ($P<em>f$) and volume ($V</em>f$) as:

  • $P<em>i V</em>i = P<em>f V</em>f$

• Charles's Law (Constant Pressure):

  • Changes in gas volume are related to changes in gas temperature (absolute temperature, Kelvin).

  • $\frac{V<em>i}{T</em>i} = \frac{V<em>f}{T</em>f}$

• Ideal Gas Law: A single statement combining Boyle's and Charles's laws.

Kinetic Theory of Gases

• A special theory developed to describe the behavior of gases.

• Three Basic Assumptions:

  1. Gas molecules are small and far apart.

  2. Gas molecules undergo elastic collisions (no loss of kinetic energy during collisions).

  3. Gas molecules are non-interacting (no forces between them, except during collisions).

• Benefits:

  • Provides a physical explanation for Boyle's and Charles's Laws.

  • Helps to better understand the concept of temperature.

• Temperature and Kinetic Energy (KE):

  • Kinetic energy is related to the motion of an object.

  • High temperature corresponds to increased molecular motion and high kinetic energy.

  • Low temperature corresponds to decreased molecular motion and low kinetic energy.

• Kinetic Theory and Phases of Matter:

  • Can describe properties of all states: Gas, Liquid, Solid, Plasma.

Phases of Matter and Changes of States

• Four Phases of Matter (in order of increasing energy):

  1. Solid

  2. Liquid

  3. Gas

  4. Plasma (most prevalent in the universe overall)

• Energy Exchange in Phase Changes:

  • Transitioning from one phase to another requires energy exchange (either consumed or released).

  • Crucially: Adding or removing energy does not cause a temperature change during a phase transition itself; the energy goes into changing the phase.

• Solid to Liquid: Melting:

  • Energy (heat) must be provided to the material.

  • This added heat does not change the temperature of the material during melting.

  • The energy increases the energy of molecules, causing them to lose their fixed positions.

  • Heat of Fusion: The heat required to change $1 \text{ kg}$ of a solid at its melting point into a liquid.

• Liquid to Solid: Freezing:

  • Energy (heat) must be removed from the material.

  • This removed heat does not change the temperature of the material during freezing.

  • As energy is removed, molecules assume more fixed positions.

  • Example: When $0^{\circ}\text{C}$ liquid water freezes into ice, the temperature of the forming ice remains $0^{\circ}\text{C}$.

• Liquid to Gas: Evaporation:

  • Takes place only near the surface of a liquid.

  • Occurs at all temperatures.

  • Molecules at the surface gain enough energy (e.g., from collisions) to become free from the liquid.

  • Since higher-energy molecules escape, lower-energy molecules are left behind, making evaporation a cooling process.

• Liquid to Gas: Boiling:

  • Takes place under the surface of a liquid.

  • Occurs only at the boiling point or higher temperatures.

  • As liquid is heated, gas bubbles form; gas inside expands, buoyant force grows, bubbles rise.

  • Bubbles form only when internal gas pressure overcomes liquid and atmospheric pressure.

  • Boiling is also a cooling process because the more energetic molecules escape.

• Effect of Pressure on Boiling:

  • The temperature of boiling water generally cannot exceed $100^{\circ}\text{C}$ unless atmospheric pressure changes.

  • Reduce Pressure $\rightarrow$ Boiling occurs at a lower temperature.

  • Increase Pressure $\rightarrow$ Boiling occurs at a higher temperature.

• Gas to Liquid: Condensation:

  • Gas molecules collide with each other and sometimes "stick together" or "coalesce" to form liquid.

  • When liquid forms, energy is released.

  • Therefore, condensation is a warming process.

• Energy "Cost" of a Phase Change:

  • Energy must be provided to or taken from a system for a phase change.

  • These energy costs are characterized by material parameters:

    • Heat of Vaporization: For liquid-to-gas changes.

    • Heat of Fusion: For solid-to-liquid changes.

Transformation of Energy: Thermodynamics

• Heat Engine:

  • Any device that transforms heat energy into mechanical energy.

  • Necessary Components:

    • A Hot reservoir (source of heat).

    • A Cold reservoir (sink for heat).

  • Heat flows from the hot reservoir to the cold reservoir.

  • A portion of this flowing heat is diverted to do useful work.

• Fundamental Laws of Thermodynamics:

  1. First Law (Conservation of Energy): Energy cannot be created or destroyed. It can only be transformed from one form to another.

  2. Second Law: All heat in a source cannot be completely transformed for work. All conversions of heat into other forms of energy are inherently inefficient.

• Maximum Efficiency:

  • The maximum efficiency of a heat engine is based on the temperature difference between the hot and cold reservoirs.

  • It is expressed as a ratio dependent on these temperatures.

• Energy Degradation Principle:

  • Any form of energy can be completely converted into heat.

  • However, only a portion of heat energy can be converted into another form of energy.

  • This implies that, overall, energy tends to be degraded into less usable forms (e.g., dispersed heat).

• Entropy:

  • A measure of disorder or randomness in any system.

  • The Second Law of Thermodynamics dictates that entropy cannot decrease in a closed system; it tends to increase or remain constant.

Quiz Questions (Summary of Key Ideas Tested)

• Heat transfer direction: FROM warmer to colder.

• Temperature relates to internal energy, average kinetic energy per atom/molecule, and is altered by heat transfer.

• Large specific heat means temperature is difficult to change.

• Internal energy can be altered by heat transfer, is the sum of all energy, and is related to temperature.

• Pressure in a fluid at a given depth is independent of the size of the container (e.g., same pressure at 3 feet deep in a pool or a lake).

• Density of a material (e.g., chocolate bar) is constant regardless of how much of the material you have (intrinsic property).

• Archimedes' Principle in action: If a ship ($10,000 \text{ kg}$ mass) is floating, the weight of the water displaced by the ship is equal to the ship's weight ($\text{Weight} = \text{mass} \times \text{g} = 10,000 \text{ kg} \times 10 \text{ m/s}^2 = 100,000 \text{ N}$).

• Loading a floating barge with material (even lightweight Styrofoam) will cause it to sink lower in the water, displacing more water to account for the increased weight.

• Touching a hot surface results in conduction heat transfer to your fingers.