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Mechanical Properties Of Fluids

Question
CBSEENPH11019523

If an ideal gas has f degrees of freedom, then what is the internal energy of gas and what will be the value of Cpand Cfor such a gas?

Solution
According to equipartition law of energy, the energy is equally distributed among all degrees of freedom.
Therefore, the internal energy of gas of one mole having f degrees of freedom is given by,
space space space space space space space space space space space space straight U space equals space straight f over 2 N k T equals straight f over 2 R T space

therefore space space space space space space straight C subscript straight v equals fraction numerator d U over denominator d T end fraction equals straight f over 2 straight R space

a n d space space straight C subscript straight p equals straight C subscript straight v plus straight R space

space space space space space space space space space space space space space space equals fraction numerator straight f plus 2 over denominator 2 end fraction straight R