Chapter 16 Thermal properties of matter Equations of state Molecular properties of matter Kinetic-molecular model of an ideal gas Heat capacity of gas Molecular speeds Phase of matter Equation of state The variables which can describe the states of material are called “ state variables”
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PV = nRT = NkBT
m = total mass
M = Molar mass
N = total number of molecules
r =density (kg/m3)
M = Molar mass (kg/mol)
y = height from sea level (m)
If y1 = 0, then
P1 = P0 =1.013 x 105 Pa
The van der Waals Equation
a and b are empirical constants
If n/V is very small
TC = Critical temperature
We try to understand the macroscopic properties of gas in terms of its atomic or molecular structure and behavior.
number of molecules =
I = 2mvx
number of molecules moving toward =
The force acting on the wall is,
I = 2mvx
Other relations :
Ktr = average translational kinetic energy of gas.
Ek= kinetic energy of one molecule.
We define the root mean square speed, vrms
M =Molar mass
In the time dt a molecule with radius r will collide with any other molecule within a cylindrical volume of radius 2r and length vdt.
The number dN with centers in this cylinder is,
number of collision per unit time
assume one molecule is moving
If all molecules are moving
The mean free time, tmean
Time that molecule can move freely
The mean free path, l
The distance that molecule can move freely.
By adding energy dQ into the system of gas, the temperature increases by dT and the kinetic energy increase by dKtr ,
CV = heat capacity at constant volume
For ideal gas point particle
3 translational df
2 rotational df
2 vibrational df
one df energy =
Equipartition of energy
“Rule of Dulong and Petit”
Triple point = the only condition under which all three phases can coexist.
Critical point = the top of the liquid-vapor equilibrium region.