`C_(p) and C_(v)` denote the molar specific heat capacities of a gas at constant volume and constant pressure respectively. Then

Options

A. `C_(p)-C_(v)` a larger to a diatomic ideal gas than for a monoatomic ideal gas.
B. `C_(p)+C_(v)` is larger for a diatomic ideal gas than for a monoatomic ideal gas.
C. `C_(p)//C_(v)` is larger for a diatomic ideal gas than for a monoatomic ideal gas.
D. `C_(p)-C_(v)` is larger for a diatomic ideal gas than for a monotomic ideal gas.

Answer

B, D

Explanation

`C_(p)-C_(v)=R` for all gases
For manoatomic gas
`C_(v)=(3)/(2) RC_(P) =(5)/(2)R=gamma ""(C_(p))/(C_(v))=(5)/(3)`
`C_(p)C_(v)=(15)/(4)C_(p)-C_(v)=4`
For diatomic gas
`C_(v)=(5)/(2)RxxC_(p) =(7)/(2)R gamma =(C_(p))/(C_(v))=(7)/(5) and C_(p)C_(v)=(35)/(4)=C_(p)+C_(v)=6`
So, correct choices are (b,d).