Specific heat at constant pressure `C_(p)` for a diatomic gas at N.T.P. in the units of cal mole k is:

Options

A. `4 cdot 95`
B. `6 cdot 93`
C. `8 cdot 93`
D. 1

Answer

B

Explanation

At N.T.P. each molecule of diatomic gas contains degrees of freedom and energy per degree of freedom
`=(1)/(2) K.T.`
`therefore` The energy of 1 molecule `=5xx(1)/(2) KT`
`therefore` 1 mole of gas contians N molecules.
`therefore` Total energy of 1 mole of diatomic gas
`U=(N cdot 5)/(2) kT. =(5)/(2) RT" "[because k=(R)/(N)]`
Since `C_(v) =(dU)/(dT)`
`C_(v)=(5)/(2) R`
`therefore C_(p) =C_(v) +R =(7)/(2) R=(7)/(2) xx1 cdot 98=6 cdot 93" cal mole"^(-1)k^(-1)`
Thus, correct choice is (b).