Question

$p V=\mu R T$ can be rewritten as

• A. $p V=k_{B} N T$ ( $N=$ total number of molecules in the perfect gas)
• B. $p=k_{B} n T$ ( $n=$ number density)
• C. $p=\rho R T / M_{0}$ ( $\rho=$ mass density and $M_{0}=$ molar mass $)$
• D. All of the above

Answer 1

Answer: (D)

The perfect gas equation can be written as
$ p V =\mu R T$
${ where, } \mu = { number of moles }$
$ { and } \, R = N_{A} k_{B}={ universal constant ... (ii) } $
$ { Here, } \mu =\frac{m}{M_{0}}=\frac{N}{N_{A}}$
where, $ m=$ mass of gas, $M_{0}=$ molar mass,
$N=$ number of molecules
and $ N_{A}=$ Avogadro's number.
Using, Eqs. (i), (ii) and (iii), we get
$p V=k_{B} N T \text { or } p=k_{B} n T$
where, $n=$ number density $=\frac{N}{V}$
Also, $p=\frac{\rho R T}{M_{0}}$
$\left[\because V=\frac{M_{0}}{\rho}\right]$
where, $\rho=$ density.
Hence, all given options are correct.