`C_v and C_p` denote the molar specific heat capacities of a gas at constant volume and constant pressure, respectively. Then

Options

A. `C_(p)-C_(v)` is larger for a diatomic ideal gas than for a monatomic 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 monoatomic ideal gas

Answer

B, D

Explanation

For monoatomic gas, `C_(p) = (5)/(2)R, C_(v) = (3)/(2)R. C_(p) - C_(v) = R`
For diatomic gas `C_(p) = (7)/(2)R, C_(v) = (5)/(2)R`
`C_(p) - C_(v) = R`
`C_(p) - C_(v)` is same for both
`C_(p) + C_(v) = 6R` (for diatmic)
`C_(p) +C_(v) = 4R` (for mono)
so `(C_(p) +C_(v))_("dia") gt (C_(p) +C_(v))_("mono")`
`(C_(p))/(C_(v)) = (7)/(5) = 1.4` (for diatomic)
`(C_(p))/(C_(v)) = (5)/(3) = 1.66` (for monoatomic)
`(C_(p)) (C_(v)) = (35)/(4)R^(2)` (for diatomic)
`(C_(p)) (C_(v)) = (15)/(4) R^(2)` (for monoatomic)
so `(C_(p).C_(v))_("diatomic") gt (C_(p).C_(v))_("monoatomic")`