The specific heat at constant pressure and at constant volume for an ideal gas are `C_(p) and C_(v)`and its adiabatic and isothermal eleasticities are `E_(phi) and E_(theta)` respectively. The ratio of `E_(phi)` to `E_(theta)` is

Options

A. `1/(C_(p)C_(v))`
B. `C_(p)C_(v)`
C. `C_(v)/C_(p)`
D. `C_(p)/C_(v)`

Answer

D

Explanation

For an ideal gas, the isothermal elasticity `(E_(i))=P`
and adiabatic elasticity `P(E_(A))=gammaP`
`thereforeE_(A)/E_(i)=gamma" "but" "gamma=C_(P)/C_(V)`
`thereforeE_(A)/E_(i)=C_(P)/C_(V)`