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Question
Show that for diatomic gas the ratio of the two specific heats is 7:5.
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Solution
- For a gas consisting of diatomic molecules such as O2, N2, CO, HCl, enclosed in a container held at a constant temperature T, if treated as a rigid rotator, each molecule will have 3 translational and 2 rotational degrees of freedom.
- According to the law of equipartition of energy, the internal energy of one mole of gas is,
E = `3/2"N"_"A""k"_"B""T" + 2/2"N"_"A""k"_"B""T"`
= `5/2"N"_"A""k"_"B""T"` - The molar specific heat at constant volume will be,
Cv = `5/2"N"_"A""k"_"B"`
= `5/2`R - Using Mayer’s relation,
Cp = R + Cv
∴ Cp = `7/2`R
∴ `"C"_"p"/"C"_"v" = 7/5`
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