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Home , Absolute zero, Ideal gas

Lecture 9

• Introduction to • scales, • changes, equilibrium, diagram Interlude

Quiz (Thursday, March 5) • Chapter 21 1st mid-term (Tuesday, March 10)

• Chapters 14, 15 (except 15.6), 20 and 21 • diverse topics: start preparing now Thermodynamics (Chs. 16-19) • Next few weeks: transformation of from one form to another: e.g. engines convert fuel energy into mechanical; living organisms convert chemical energy of food into kinetic... macroscopic systems instead of particles; temperature (T), (p)...instead of position, velocity... How do pressure, temperature change or done by engines related to fuel energy used? macro/micro connection: T related to of ...2nd law... ultimate goal: how engines convert heat energy to work • This week bulk properties (T, p) phases of matter; phase changes start micro/macro connection • Today: 3 phases of matter; mass... , and change between liquild/ or /: phase change • Solids rigid: atoms vibrate, but not free to move; incompressible (atoms as close as can be); crystal (arranged in periodic arrray) or amorphous (random) • Liquids incompressible, but flows/fits shape of container: molecules can slide around each other, but can’t get far apart • Gases freely moving molecules...till collide with each other/wall compressible (lot of space...) State variables parameters describing macroscopic systems e.g. • M mass (M), (ρ ), p, T...related: e.g., ρ = V change state by changing variables: ∆X = X X • f − i • Thermal equilibrium: state variable not changing

Atoms and Moles (I)

• mass depends on total number of atoms, N, typically 1025, i.e., 1024 to 1026 105 or 1015 ∼ " : larger in solid than gas, independent of for uniform system Atoms and Moles (II) • mass of determined by atomic mass number (number of protons and neutrons) • atomic mass unit: mass of 12 C atom (6 p + 6 n) defined to be 12 u m 1 /m 12 = 1.0078 m 1 =1.00078u H C 12 → H m 1 A (neglect small difference) ! H" ≈ ! " ! " • molecular! " mass: sum of atomic masses • 1 contains Avogadro’s number: 6 . 02 10 23 of basic particles 12 × 23 (as in12 g of C ): e.g. 1 mole of O 2 :2 6 . 02 10 O atoms number of moles, × × 12 g 26 1 atom of 12C has mass 6.02 1023 =1.993 10− kg × × m 12 C 27 1 u = =1.661 10− kg ⇒ “12 ” × 26 m 20 = 20 u =3.32 10− kg Ne × ( ): mass in grams of 1 mole (12 g/mol. for 12 C ) • ! " Mmol. = atomic mass in u Temperature • temperature is related to system’s (kinetic and of atoms) • measured by : small system undergoes a change upon exchagning thermal energy, e.g., length of mercury/alcohol in glass tube or ’ pressure Temperature Scales • Celcius/centigrade scale: boiling point (100 C ) freezing point (0 C ) ◦ ◦ T = 9 T + 32 • scale: F 5 C ◦ F (212 ◦ and 32 ◦ F ) Example • At what temperature does the numerical value in Fahrenheit in match the numerical value in degree ? Absolute Zero and Absolute Temperature • property changes linearly with temperature: e.g., pressure of constant-volume gas

p = 0 for all gases at T = 273 C • 0 ◦ p due to all motion− stopped, zero thermal energy: absolute zero (lowest temperature) • absolute temperature scale: zero point at absolute zero scale if same unit size as Celcius scale:

TK = TC + 273 (no degrees for Kelvin) Phase Changes • melting/freezing point: temperature at which solid becomes liquid...thermal energy large enough to allow molecules to move around • phase equilibrium: 2 phases co-exist • /boiling point: phase equilibrium between liquid and gas thermal energy too large for bonding • phase change are pressure-dependent: freezing (boiling) point higher (lower) at lower pressure Phase diagram • how phases and phase changes vary with T, p • 3 regions with phase transitions at boundaries...gas-solid (sublimation) • critical point: liquid-gas boundary ends • : all 3 phases co-exist • triple point of water ( T =0 . 01 C ) used as reference 3 ◦ point (reproduced with no variation) for Kelvin scale: 273.16 K 0 K fixed by gas properties • cf. Celcius scale requires 2 reference points: boiling and melting points (p-dependent)