The specific heat of argon at constant pressure and constant volume are $C_p$ and $C_v$ respectively. It's…

The specific heat of argon at constant pressure and constant volume are $C_p$ and $C_v$ respectively. It's density ' $\rho$ ' at N.T.P. will be [ P and T are pressure and temperature respectively at N.T.P.]
  1. $\frac{P}{T\left(C_p-C_v\right)}$
  2. $\frac{\mathrm{PT}}{\left(\mathrm{C}_{\mathrm{p}}-\mathrm{C}_{\mathrm{v}}\right)}$
  3. $\frac{\mathrm{T}\left(\mathrm{C}_{\mathrm{p}}-\mathrm{C}_{\mathrm{v}}\right)}{\mathrm{P}}$
  4. $\frac{\left(C_p-C_v\right)}{\text { PT }}$

Solution

$\begin{aligned} & C_p-C_v=R \\ & R=\left(C_p-C_v\right) M \quad \text {...(molar specific heat) } \end{aligned}...(i)$
Ideal gas equation, $\mathrm{PV}=\mathrm{nRT}$ $\begin{aligned} & P V=n\left(C_p-C_v\right) M T \\ & P V=\frac{m}{M}\left(C_p-C_v\right) M T \\ & P=\frac{m}{V}\left(C_p-C_v\right) T \\ & \rho=\frac{P}{\left(C_p-C_v\right) T} \end{aligned}$ ...[From(i)]

Asked in: MHT CET 2024 (03 May Shift 2)

Practice more Thermodynamics questions on Aicharya