Vander waals equation
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B.Sc. Physics THERMODYNAMICS Why a fog appears just after opening a bottle of a cold drink? When the bottle of cold drink (Carbonated drink) is opened. The pressure inside the bottle drops and hence the temperature inside the bottle also decreased, due to which the amount of moisture that air can hold also drops. Then due to condensation the droplets of water condense out of the air and the fog is appears just after opening the bottle. DEGREE OF FREEDOM It is defined as the number of possible independent ways in which a system can have energy. EQUIPARTITION OF ENERGY Equipartition of energy is basically a theorem that derived by James Clark Maxwell according to which; “When the number of molecules is large, the average energy per molecule is 1 2 kT for each independent degree of freedom” Simply we can say “Each degree of freedom contributes 1 2 kT to the internal energy.” INTERNAL ENERGY OF AN IDEAL GAS The total internal energy of “n” moles of an ideal gas can be written as the number of molecules (=n N A ) times the average energy per molecule: U=E ∫ ¿= ( nN A)( K trans ) =(nN A )( f 2 kT) ¿ U=E ∫ ¿= f 2 nRT¿ Where f is the degree of freedom. For monoatomic gas f = 3 U=E ∫ ¿= 3 2 nRT¿ For diatomic gas f = 5 U=E ∫ ¿= 5 2 nRT¿ For polyatomic gas f = 6 U=E ∫ ¿= 6 2 nRT=3 nRT¿ Muhammad Azhar (MS Physics, NEDUET) [email protected]
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Transcript of Vander waals equation
B.Sc. Physics THERMODYNAMICS Why a fog appears just after opening a bottle of a cold drink?
When the bottle of cold drink (Carbonated drink) is opened. The pressure inside the bottle drops and hence the temperature inside the bottle also decreased, due to which the amount of moisture that air can hold also drops. Then due to condensation the droplets of water condense out of the air and the fog is appears just after opening the bottle.
DEGREE OF FREEDOM
It is defined as the number of possible independent ways in which a system can have energy.
EQUIPARTITION OF ENERGY
Equipartition of energy is basically a theorem that derived by James Clark Maxwell according to which;
“When the number of molecules is large, the
average energy per molecule is 12
kT for each
independent degree of freedom”
Simply we can say “Each degree of freedom
contributes 12
kT to the internal energy.”
INTERNAL ENERGY OF AN IDEAL GAS
The total internal energy of “n” moles of an ideal gas can be written as the number of molecules (=nN A) times the average energy per molecule:
U=E∫¿=(n NA ) ( K trans )=(n N A)(
f2
kT )¿
U =E∫¿= f
2nRT ¿
Where f is the degree of freedom.
For monoatomic gas f = 3
U =E∫¿= 3
2nRT ¿
For diatomic gas f = 5
U =E∫¿= 5
2nRT ¿
For polyatomic gas f = 6
U=E∫¿= 6
2nRT=3 nRT ¿
Muhammad Azhar (MS Physics, NEDUET) [email protected]
B.Sc. Physics THERMODYNAMICS
KINETIC MOLECULAR THEORY OF GAS
REAL GAS: Vander Waals Equation of State
The ideal gas law works if the gas density is low enough. For many real gases, however, the ideal gas is not a good approximation. In those cases, we must use the Vander Waals Equation of state, which frees us from two of the assumptions of the kinetic theory:
1. The molecules are particles with no physical extant2. The molecules only exert contact forces on one another
The assumption 1 can be disregarded as we model gas molecules as sphere of radius “r”.
The assumption 2 can be also disregarded as the molecules actually exert an attractive on one another due to electromagnetic force.
Think about the motion of a single gas molecule. It cannot move through the entire volume “V” of the container because other molecules take up some of that volume. We can write the relation:
V availble=V−V molecules
For convenient we can write the volume occupied by the molecules in terms of “b” is the volume of molecule per mole. The volume occupied by the molecules is then the number of moles “n” multiplied by “b”.
V availble=V−nb
Because molecules takes up some volume, we correct the ideal gas law PV =nRT as:
PClausius(V−nb)=nRT
Above equation known as Clausius Equation of State.Muhammad Azhar (MS Physics, NEDUET) [email protected]
B.Sc. Physics THERMODYNAMICS This equation models the molecules as sphere “r”, but it does not take into account the field force they exert on one another.
We can modify the Clausius Equation of State to include that attractive filed force. Imagine the motion of one molecule as it approaches one of the container’s walls, where it pulled back by attractive force of the other molecules. The force molecule exerts on the wall is smaller than it would be if there were no field forces. Because all the molecules experience such a force, the pressure exerted on the walls is reduced:
P=PClausius−P reduction
Muhammad Azhar (MS Physics, NEDUET) [email protected]
