p V=μ R T can be rewritten as

Question

p V=μ R T can be rewritten as (A) p V=kB N T ( N= total number of molecules in the perfect gas) (B) p=kB n T ( n= number density) (C) p=ρ R T / M0 ( ρ= mass density and M0= molar mass ) (D) All of the above

Tardigrade Admin · Accepted Answer

The perfect gas equation can be written as

p V = μ RT

w h ere, μ = n u mb ero f m o l es

an d R = N_{A} k_{B} = u ni v ers a l co n s t an t ... (ii)

Here, μ = \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} NT or p = k_{B} n T

where,

n =

number density

= \frac{N}{V}

Also,

p = \frac{ρRT}{M _{0}}

[∵ V = \frac{M _{0}}{ρ}]

where,

ρ =

density.
Hence, all given options are correct.

Q. $p V = μ RT$ can be rewritten as

$p V = k_{B} NT$ ( $N =$ total number of molecules in the perfect gas)

$p = k_{B} n T$ ( $n =$ number density)

$p = ρRT / M_{0}$ ( $ρ =$ mass density and $M_{0} =$ molar mass $)$

All of the above

Q. pV=μRT can be rewritten as

pV=kB​NT ( N= total number of molecules in the perfect gas)

p=kB​nT ( n= number density)

p=ρRT/M0​ ( ρ= mass density and M0​= molar mass )

All of the above

Q. $p V = μ RT$ can be rewritten as

$p V = k_{B} NT$ ( $N =$ total number of molecules in the perfect gas)

$p = k_{B} n T$ ( $n =$ number density)

$p = ρRT / M_{0}$ ( $ρ =$ mass density and $M_{0} =$ molar mass $)$