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Lecture 10
• Ideal gas model
• Ideal gas law
• Quasi-static processes: isochoric, isobaric and isothermal
Ideal Gases• (strong) repulsive forces between atoms
(incompressibility of solids/liquids + (weak) attractive forces (tensile strength of solids; cohesion of liquid droplets)
• solids and liquids: atomic separation
• gases: freely moving till collide (steep wall for important)
• Ideal gas model: hard non-interacting spheres, bounce on contact
• good for low density and condensation point
! req
(both mono and d-atomic gases)
average r ! req
T !
r < req.
Ideal-gas law• Experiments state variables not independent: for all gases
• Gases in sealed containers (n constant)
• Using,
• typical p, V, T: average distance between gas molecules distances over which atoms exert attractive forces
universal gas constant, R = 8.31 J/mol/K
Boltzmann's constant, k_B = R/N_A = 1.38 x 10^(-23) J/K
= p / k_B T
!
Example
• 3.0 mol of gas at a temperature of -120 degrees Celsius fills a 2.0 L container. What is the gas pressure?
Ideal gas processes (how gas changes state)• diagram: each point is unique
state of gas (T by ideal-gas law; n known for sealed container) (p, V, T)
• ideal gas process: trajectory showing intermediate states (work done depends on it)
• Quasi-static processes: slow; system in thermal equilibrium at all times
(reversible)
pV
(i) Isochoric (constant V) process
• : vertical line on diagramVf = Vi pV
(ii) Isobaric (constant p) process
• gas pressure from balancing of forces on piston
• : horizontal line on diagram
(expansion: compression if cooled)
pf = pi
p = patmos + MgA
pV
(iii) Isothermal (constant T) process• heat transfer keeps gas at same T as liquid
• : hyperbola on diagram (inverse relationship)
• location of hyperbolae (isotherms) depends on T: lower T, closer to origin
Tf = Ti and pV = nRT ! piVi = pfVf
p = nRTV = constant
V pV
Example• A rigid container holds hydrogen gas at a pressure of
3.0 atm and a temperature of 2 degrees Celsius. What will the pressure be if the temperature is raised to 10 degrees Celsius?