Boyle’s Law
Imagine you press on an airtight plunger
- The displacement causes compression of a gas reducing the volume of the system
If the plunger is forced to prevent movement, the pressure of your hand equals the pressure
of gas under compression
- This inverse relationship is Boyle’s law + requires 2 functions of state; volume +
pressure
- Therefore pV = constant
Charles Law
Place that plunger in a heat bath, as the temperature rises so does the plunger
- As the temperature lowers, the gas contracts lowering the volume
- Thus, V= constant x T
- Or constant = V/T
Gay-Lussac’s Law
- This shows that pressure is proportional to pressure
The experiment is a combination of the plunger + heat bath experiments
Avogadro’s Law
The volume of a fluid is proportional to the amount of fluid
- Therefore equal volumes of all gases of the same temperature and pressure have the
same number of molecules
- This is an essential precursor to Avogadro’s constant
Clapeyron’s Connection
This made connections between pressure, volume and temperature
- pV is proportional to T
- pV = constant x T
- pV = nRT
Equilibrium
- This is required for the ideal gas law
- All states require equilibrium
Chemical equilibrium = no overall change to overall composition, but the reaction can still
occur
- Defined as reached when there is no measurable change
,Temperature is very measurable and mechanically defined using modified plungers
- If A and b have the same composition nA = nB
- But if gas B is at a higher temp, TA < TB
- Since there is no thermal contact heat can’t transfer, so VA < VB
If the vacuum was replaced by thermally conductive metal, they fall into thermal
equilibrium
- nA = nB
- TA = TB
- VA = VB
Imagine Four Boxes of Fixed Volume with Thermal Contact
- nA = nB = nC = nD
- TA = TB = TC = TD
- Therefore pAVA = pBVB = pCVC = pDVD
Zeroth Law of Thermodynamics
If 3 bodies, A,B and C where A and C are separately in thermal equilibrium with B, then A
and C are in thermal equilibrium with one another
- It seems obvious but it is the basis of all thermometers
- Thermal equilibrium = same temperature
Thermometer Scales
Celsius = 0 is freezing and 100 is boiling
Fahrenheit = 0 is the coldest place on Earth, 100 is the hottest place
- The issue is they are both subjective, what about different pressures or extreme
places
Thus Kelvin is the best scale
- Pressure is plotted against temperature to produce a straight line
- Therefore when T = 0, p = 0 with a fixed point through origin
- 1K = 1 celcius
- -273.15 between C and K
, Energy May be Interconverted
If you let go off a book, the acceleration generates kinetic energy (K)
- That energy came from somewhere, stored as potential enrgy (V)
- So energy is transferred
What happens when the book lands?
- Energy is conserved and redistributed
If the system is the book, the energy seems to be destroyed
If the system is the room, no energy has left or entered
Energy Stored Within Chemical States
For example, when sodium is added to water, there is a flash, band and heat
- This is seen as chemical energy
- Reallocation of bonds and electrons produced are energetically more stable than the
reagents
Other Systems
- Isolated = no energy or matter transfer
- Closed = energy transfer but no matter transfer
- Open = energy + matter transfer
The system is part of the world we are interested in, everything else is the surrounding
- Kinetic and potential energy are macroscopically observable, internal energy
accounts for the microscopic consideration
E=T+V+U
- Where energy = kinetic + potential + internal
Heat
- The movement of energy until thermal equilibrium is reached
Remember the plungers connected by thermally conductive metal of different temps
- No particles are exchanged
Thermal energy always moves from hotter to colder until thermal equilibrium is reached
- Flow – heat, q
Heat Can Move into a System
In a plunger/heatbath with no hands the plunger expands when temperature of the bath is
larger than the plunger
- If the plunger is seen as the system + others are the surrounding the world would be
very different
Delta
= different, end point – beginning point
Rate = y/x
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