For a certain gas the heat capcity at constant pressure is greater than that at constant volume by `29.1 J//K`.
(a) How many moles of the gas are there ?
(b) if the gas is monatomic, what are heat capacities at constant volume and pressure ?
( c) If the gas molecules are diatomic which rotate but do nit vibrate, what are heat capacities at constant volume and at constant pressure.

Answer

A, B, C

Explanation

(a) Molar heat capacity `C_p = (Q)/(n Delta T)`
and heat capacity `C_p = (Q)/(Delta T)`
`:. C_p = n C_ P`
Similarly, `C_v = n C_V`
now, `C_p - C_v = n(C_p - C_V) - n R`
`:. n = (C_p - C_v)/(R) = (29.1)/(8.31) = 3.5 `
(b) `C_p = n C_p = n(5/2R)`
=`(3.5)(2.5)(8.31)`
= `72.75 J//K`
`C_v = n C_V = n(3/2 R)`
= `(3.5)(1.5)(8.31)`
= `43.64 J//K`
( c) `C_p = n C_p = n (7/2 R)`
=`(3.5)(3.5)(8.31)`
= `101.8 J//K`
`C_v = n C_V = n(5/2 R)`
= `(3.5) (2.5)(8.31)`n
= `17.75 J// K`.