The molar specific heat at constant pressure of an ideal gas is `(7//2 R)`. The ratio of specific heat at constant pressure to that at constant volume is

Options

A. ` 7//5 `
B. ` 8//7 `
C. ` 5//7 `
D. ` 9//7 `

Answer

A

Explanation

Molar specific heat at constant pressure
` C_p = ( 7 ) /( 2 ) R `
Mayer's relation can be written as
` rArr C_p - C _V = R `
` C _ V = C _ P - R = ( 7 ) /( 2 ) R - R = ( 5 ) / ( 2 ) R `
Hence, required ratio is
` gamma = ( C_p )/ ( C_V) = (( (7 ) /( 2 )) R)/( (( 5 )/( 2 )) R ) = ( 7 ) /( 5 ) `