Q138 / 160 · AP EAMCET 2019 (23 Apr Shift 1) · Physics

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

  • A
    \(2.88 \mathrm{kgm}^{-3}\)
  • B
    \(4.86 \mathrm{kgm}^{-3}\)
  • C
    \(3.88 \mathrm{kgm}^{-3}\)
  • Correct answer
    D
    \(1.86 \mathrm{kgm}^{-3}\)

Solution

Given, specific heat capacity of a gas at constant pressure, \(C_p=620 \mathrm{~J} \mathrm{~kg}^{-1} \mathrm{~K}^{-1}\) and specific heat capacity of gas at constant volume, \(C_V=420 \mathrm{~J} \mathrm{~kg}^{-1} \mathrm{~K}^{-1}\) \(\because\) Molar specific heat of gas at constant pressure and constant volume are given by \(\therefore \quad C_p{ }^{\prime}=m C_p=m(620)\) and \(\quad C_V{ }^{\prime}=m C_v=m(420)\) As we know that, \(\because \quad C_p{ }^{\prime}-C_V{ }^{\prime}=R\) [Here, \(R\) = universal gas constant] \(\begin{aligned} m[620-420] & =R \\ \Rightarrow \quad m & =\frac{R}{200} \qquad \ldots (i) \end{aligned}\) Now, ideal gas equation, \(p V=\mu R T\) where, \(\mu=\) number of moles of gas or \(\begin{aligned} & p V=R T \quad[\because \text { for } 1 \text { mole, } \mu=1] \\ & \therefore \quad p m=\rho R T \quad\left[\because \text { density, } \rho=\frac{m}{V}\right] \\ & 10^5 \times \frac{R}{200}=\rho R(273) \quad \text { [From Eq. (i)] } \\ & \rho=1.85 \mathrm{Kg}-\mathrm{m}^{-3} \end{aligned}\) Hence, the option (d) is correct.

Hence, the correct answer is option: 'D'.

Relevant Questions