Specific heats, as derived by Bill's equation, only work for monatomic molecules. this is because the only place for monatomic molecules to 'put' their energy is into the kinetic energy of motion.
As soon as we have a polyatomic molecule energy can be distributed into other modes such as stretching, vibration and rotation of the bonds.
Unfortunately things get more complicated than this because the dear old Quantum Theory rears its head at this point and requires that the specific heats of polyatomic molecules ivary with temperature, whereas in a purely mechanical model they remain constant.
Some real world values for Cv are
Monatomic helium..............12.48 ; 12.48
Diatomic oxygen................21.05 ; 21.79
Triatomic hydrogen dioxide...25.25 ; 25.93
Triatomic carbon dioxide.......28.81 ; 33.00
all figures in joules per degree K per mole. the first at 298°K and the second at 400°K in each case.
As soon as we have a polyatomic molecule energy can be distributed into other modes such as stretching, vibration and rotation of the bonds.
Unfortunately things get more complicated than this because the dear old Quantum Theory rears its head at this point and requires that the specific heats of polyatomic molecules ivary with temperature, whereas in a purely mechanical model they remain constant.
Some real world values for Cv are
Monatomic helium..............12.48 ; 12.48
Diatomic oxygen................21.05 ; 21.79
Triatomic hydrogen dioxide...25.25 ; 25.93
Triatomic carbon dioxide.......28.81 ; 33.00
all figures in joules per degree K per mole. the first at 298°K and the second at 400°K in each case.