The specific heat capacities of an ideal gas at the constant pressure and at constant volume are `620 Jkg^(-1) K^(-1)` and `420 Jkg^(-1) K^(-1)` respectively. The density of the gas at STP is approximately,

Options

A. `2.88 kgm^(-3)`
B. `4.86 kg m^(-3)`
C. `3.88 kg m^(-3)`
D. `1.86 kg m^(-3)`

Answer

D

Explanation

Given, specific heat capacity of a gas at constant pressure, `C_(p) = 620 J kg^(-1) K^(-1)`
and specific heat capacity of gas at constant volume, `C_(v) = 420 J kg^(-1) K^(-1)`
`because` Molar specific heat of gas at constant pressure and constant volume are given by
`:. C_(p). = mC_(p) = m(620)`
and `C_(V). = mC_(V) = m(420)`
As we know that,
`because C_(p). = C_(V). = R`
[Here, R = universal gas constant]
`m[620 - 420] = R`
`rArr m = (R )/(200)` ...(i)
Now, ideal gas equation,
`pV = mu RT`
where, `mu` = number of moles of gas
or `pV = RT " " [because "for 1 mole", mu = 1]`
`:. p m = rho RT " "[because "density ", rho = (m)/(V)]`
`10^(5) xx (R )/(200) = rho R(273)` [From Eq. (i)]
`rho = 1.85 Kg-m^(-3)`
Hence, the option (d) is correct.