Final exam

Final exam

1. Ch. 14: Temperature and Heat

   • Zeroth law of thermodynamics
     • If systems A and B are in thermal equilibrium and systems B and C are in thermal equilibrium, systems A and C are in thermal equilibrium.
     • Temperature is a unique property that determines thermal equilibrium.
       • Three different temperature scales:
         • Fahrenheit
         • Celsius
         • Kelvin
   • Heat
     • Heat flow: transfer of energy from one object to another by virtue of a temperature difference
       • Heat conduction
         • Determined by thermal conductivity, κ
           • (Q/T)=κA(ΔT/L)
             • Q=heat energy transferred in time t
             • L=length of the system
             • A=cross-sectional area of the system
       • Convective heat flow
         • Involves the movement of mass and is caused by thermal expansion and contraction
       • Radiative heat flow
         • Involves electromagnetic radiation
           • The total amount of energy an object radiates depends on its temperature.
             • Stefan-Boltzmann law
               • An object with surface area A and temperature T radiates energy at a rate Q/t
                 • (Q/t)=σeAT^4
             • Wien's law
               • The wavelength at which radiation is strongest depends on temperature.
                 • λmax=(2.90•10^-3 m•K)/T
               • Explains why the color of a glowing object depends on its temperature
   • Specific heat and latent heat
     • If an amount of heat energy Q is added to a substance with mass m, the temperature increases by an amount ΔT
       • Q=cmΔT
         • c=specific heat
         • This equation applies if there is no phase change.
           • If there is a phase change such as melting or evaporation, a certain amount of energy called the latent heat must be added to or taken from the system.
   • Thermal expansion
     • When the temperature of a substance changes, its physical dimensions usually change.
       • Changes in length are proportional to the coefficient of thermal expansion α
         • (ΔL/Lo)=αΔT
       • Changes in volume are proportional to the coefficient of volume expansion β
         • (ΔV/Vo)=βΔT

2. Ch. 15: Gases and Kinetic Theory

   • Kinetic theory
     • Kinetic theory is the application of Newton's laws to the mechanics of a gas of particles
       • Leads to the ideal gas law
         • For a dilute gas composed of any substance, PV=nRT
           • P=pressure, V=volume, n=number of moles of particles, T=temperature, R=universal gas constant=8.31 J/(mol•K)
         • Can also be written PV=N(kB)T
           • N=number of particles
           • kB=Boltzmann's constant=1.38•10^-23 J/K
   • Internal energy
     • The temperature of a dilute gas is related to the average kinetic energy of a molecule
       • KE=(3/2)(kB)T
       • The internal energy of a monatomic ideal gas is equal to the total kinetic energy of the molecules
         • U=(3/2)N(kB)T
           • For an ideal gas, U is independent of the molecular mass and pressure.
   • Gas laws
     • The ideal gas law contains several other gas laws as special cases.
       • Boyle's law
         • For a sample of gas at a constant temperature, the product of the pressure and the volume is constant.
           • PV=constant
       • Charles's law
         • For a sample of gas at constant pressure, if the temperature is changed by a small amount ΔT, the volume changes by an amount ΔV
           • ΔV α ΔT
       • Gay-Lussac's law
         • For a sample of a gas held in a container with a constant volume, changes in pressure are proportional to changes in temperature.
           • ΔP α ΔT
       • Avogadro's law
         • For a sample of gas at a constant pressure and temperature, the volume is proportional to the number of molecules in the sample.
   • Specific heat of a gas
     • Specific heat per mole of a monatomic ideal gas at constant volume: Cv=(3/2)R
   • Diffusion
     • The random motion of individual gas molecules
       • Δr=√(Dt)
         • Δr=average net distance that a molecule diffuses in time t
         • D=diffusion constant

3. Ch. 16: Thermodynamics

   • Concerned with the behavior of systems containing many particles such as a liquid, gas, or solid.
   • Zeroth law of thermodynamics
     • If two systems A and B are both in thermal equilibrium with a third system, then A and B are in thermal equilibrium with each other.
   • First law of thermodynamics
     • If an amount of heat Q flows into a system from its environment and an amount of work W is done by the system on its environment, the internal energy of the system changes by an amount ΔU=Uf-Ui=Q-W
   • Second law of thermodynamics
     • Can be stated in several different ways.
       • Formulation involving heat flow
         • Heat flows spontaneously from a warm object to a colder one. It is not possible for heat to flow spontaneously from a cold object to a warmer one.
       • Formulation involving heat engines
         • The efficiency of a reversible heat engine operating between reservoirs at temperatures T(H) and T(C)
           • e=1-T(C)/T(H)
             • No heat engine can have a greater efficiency.
       • Entropy
         • In any thermodynamic process, ΔS(universe)≥0
   • Third law of thermodynamics
     • It is impossible for the temperature of a system to reach absolute zero.
   • Thermodynamic processes
     • Isothermal: Temperature remains constant
     • Adiabatic process: No heat flow into or out of the system. Q=0