- Gas Laws
- Ideal gas equation
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- Moleular nature of matter
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- Dalton's law of partial pressures
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- Kinetic Theory of an ideal gas
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- Pressure of gas
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- Kinetic interpretation of temperature
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- Law of Equipartition of energy
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- Specific Heat Capacity
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- Specific heat Capacity of Solids
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- Mean free Path
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- Solved examples

- Monoatemic gas moleules has three translational degrees of freedom.

- From law of equipartition of energy average energy of an molecule at temperature T is (3/2)K
_{B}T

- Total internal energy of one mole of such gas is

U= (3/2)K_{B}TN

= (3/2) RT (12)

- If C
_{V}is melar specific heat at constant volume then

C_{V}v = dU/dT

= (3/2)R (13)

now for an ideal gas

C_{P}- C_{V}= R

C_{P}- molar specific heat capacity at constant presseve

C_{P}= 5/2 R (14)

Thus for a monoatomic gas ratio of specific heats is

γ_{mono}= C_{P}/C_{V}= 5/3 (15)

- A diatomic gas molecule is treated as a rigid rotator like dumb-bell and has 5 degrees of freedom out of which three degrees of freedom are translatoinal and two degrees of freedom are rotational.

- Using law of equipartition of energy the total internal energy of one mole of diatomic gas is

U= (5/2)K_{B}TN

= (5/2) RT (16)

- Specific heats are thus

C_{V}=(5/2)R

γ_{dia}= 5/7 (rigid rotater)

- If diatomic molecule is not only rigid but also has an vibrational mode in addition, then

U = (7/2) RT

and C_{V}=(7/2)R

C_{P}=(9/2)R

and γ=C_{P}/C_{V}=9/7

- From law of equipartation of energy we can can also determine specific heats of solids.

- Consider that atoms in a solid are vibrating about their mean position at some temperature T.

- Oscillation in one dimension has average energy equals 2(1/2)K
_{B}T=K_{B}T, as (1/2)K_{B}T is PE and (1/2)K_{B}T is KE of the atom.

- In three dimensions average kinetic energy is 3K
_{B}T.

- For one mole of solid total energy is

U= 3NK_{B}T

= 3RT

- At constant pressure ΔQ =ΔU+PΔV=ΔU since for solids ΔV is negligible hence

C=ΔQ/ΔT=ΔU/ΔT=3R

- This is Dulang and Petit law.

- Here we note that predictions of specific heats of solids on the basis of law of equipetation of energy are independent of temperature.

- As we go towards low temperatures T→0 there is a pronounced departure from the value of specific heat of solids as calculated.

- It is seen that specific heats of substance aproaches to zero as T→0.

- This result can further be explained using the principles of quantum mechanics which is beyond our scope.

Class 11 Maths Class 11 Physics Class 11 Chemistry

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