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Question
Show that for monoatomic gas the ratio of the two specific heats is 5:3.
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Solution
- For a monatomic gas enclosed in a container, held at a constant temperature T, and containing NA atoms, each atom has only 3 translational degrees of freedom.
- Therefore, the average energy per atom is `3/2` kBT and the total internal energy per mole is, E = `3/2` NAkBT
- Molar specific heat at constant volume
Cv = `"dE"/"dT" = 3/2"N"_"A""k"_"B" = 3/2"R"` - Using Mayer’s relation, CP = R + CV
∴ Cp = `5/2`R
∴ `"C"_"p"/"C"_"v" = 5/3`
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