Define Cp and Cv. Derive an erpression for the ratio of Cp/Cv for a diatomic gas.
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нєу тнєяє ιѕ αиѕωєя !!
ι нσρє уσυ нєℓρ !!
ρяσσf = ¢ρ & ¢ν
Dear studentFrom the law ofequipartition of energy on an average kinetin energy of one atom for one degree of freedom is 12kT (where k is Boltzmans constant).So kinetic energy of one mole of atom for f degree of freedom is NA×f×12kT (where k is Boltzmans constant and NA is avagadros number T is absolute temperature).So kinetic energy of n mole of gas for f degree of freedom is NA×f×n×12kT ...1For ideal gas there is no intermolecular force of attraction so there is no potential energy ,internal energy of ideal is the total kinetic energy.Internal energy of ideal gas=ncvT ....2 (where n is number of mole cv is molar heat capacity at constant volume)From equation 1 and 2NA×f×n×12kT=ncvTk=RNANA×f×n×RNA×12T=ncvTf×R×12=cvcv=f×R×12...3Degree of freedom f of monoatomic ideal gas is f=3 , cv=3×R2 (monoatomic ideal gas) and cp−cv=R cp=R +3×R2 =5R2 Degree of freedom f of diatomic ideal gas is f=5 From eqn ...3cv=fR2 cv=5×R2 andcp=cv+R=5×R2+R=7R2Regards
ι нσρє уσυ нєℓρ !!
ρяσσf = ¢ρ & ¢ν
Dear studentFrom the law ofequipartition of energy on an average kinetin energy of one atom for one degree of freedom is 12kT (where k is Boltzmans constant).So kinetic energy of one mole of atom for f degree of freedom is NA×f×12kT (where k is Boltzmans constant and NA is avagadros number T is absolute temperature).So kinetic energy of n mole of gas for f degree of freedom is NA×f×n×12kT ...1For ideal gas there is no intermolecular force of attraction so there is no potential energy ,internal energy of ideal is the total kinetic energy.Internal energy of ideal gas=ncvT ....2 (where n is number of mole cv is molar heat capacity at constant volume)From equation 1 and 2NA×f×n×12kT=ncvTk=RNANA×f×n×RNA×12T=ncvTf×R×12=cvcv=f×R×12...3Degree of freedom f of monoatomic ideal gas is f=3 , cv=3×R2 (monoatomic ideal gas) and cp−cv=R cp=R +3×R2 =5R2 Degree of freedom f of diatomic ideal gas is f=5 From eqn ...3cv=fR2 cv=5×R2 andcp=cv+R=5×R2+R=7R2Regards
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