Prepared
by Dr. A. Mekki
Summary
of chapter 20
_{}
where N is the number of
molecules, m is the mass of the substance, M is the molar mass of the substance
and N_{A} is Avogadros number.
N_{A} = 6.02 x 10^{23}
molecules/mole (is the number of molecules in ONE mole of the substance).
_{} The ideal gas law
R = 8.31 J/mole K, is the
gas constant and n is the number of moles of the gas.
We have three situations
(i) Temperature constant (isothermal process) _{}
(ii) Volume constant (isochoric process) _{}
(iii) Pressure constant (isobaric process) _{}
In the above equations T in Kelvin.
_{} T
in Kelvin
For an isobaric
process, the work
done on or by the gas is
W =
P DV
If V_{f }> V_{i}
(expansion), then W > 0, the gas do work
If V_{f} < V_{i}_{ }(compression),
then W < 0, external work is done on the gas.
_{}
where v_{rms}
is the rootmeansquare speed of the gas molecules = _{}
This
speed is related to the molar mass and the temperature of the gas as
follows:
_{} T in Kelvin
_{} T in Kelvin
k =
1.38 x 1023 J/K is Boltzman constant.
_{} T in Kelvin
Therefore
the change in internal energy is
_{}
So: for an isothermal process the change in
internal energy of the gas is ZERO because DT = 0.
(i)
for a constant volume
process (isochoric) the heat is given by
_{}
(ii)
for a constant pressure
process (isobaric) the heat is given by
_{}
_{}
_{} T
in Kelvin
where _{} is the specific heat ratio (constant).
_{}
Process 
PV diagram 
W 
Q 
DE_{int} 
Isothermal 

_{} 
_{} 
0 
Isobaric 

P DV 
n C_{p} DT 
n C_{v} DT 
Isochoric 

0 
n C_{v} DT 
n C_{v} DT 
Adiabatic 

 n C_{v} DT 
0 
n C_{v} DT 
Cyclic 

Area enclosed 
Area enclosed 
0 
Note:
_{} This is ALWAYS
true, for all processes!
Gas 
C_{v}

C_{p} 
g
= C_{p}/C_{v} 
Monoatomic 
3/2 R 
5/2 R 
1.67 
Diatomic 
5/2 R 
7/2 R 
1.4 
C_{p} = C_{v}
+ R