MHT CET · Physics · Thermodynamics
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.]
- A \(\frac{P}{T\left(C_p-C_v\right)}\)
- B \(\frac{\mathrm{PT}}{\left(\mathrm{C}_{\mathrm{p}}-\mathrm{C}_{\mathrm{v}}\right)}\)
- C \(\frac{\mathrm{T}\left(\mathrm{C}_{\mathrm{p}}-\mathrm{C}_{\mathrm{v}}\right)}{\mathrm{P}}\)
- D \(\frac{\left(C_p-C_v\right)}{\text { PT }}\)
Answer & Solution
Correct Answer
(A) \(\frac{P}{T\left(C_p-C_v\right)}\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned}
& C_p-C_v=R \\
& R=\left(C_p-C_v\right) M \quad \text {...(molar specific heat) }
\end{aligned}...(i)\)
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)]
& 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)]
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