For a gas of N identical molecules of molecular volume V_m in total volume V at temperature T,the number of ways of locating the N molecules in the volume is

Question

Quizplus · Accepted Answer

The number of ways of locating the N molecules in the volume is given by:
W=N!/(n1!n2!....nk!) *(V/n)^N
where ni is the number of molecules in the i-th subvolume of V divided into N subvolumes of equal volume V/N.
Here, we have only one subvolume, so k=1, ni=N, V/n=Vs (volume per molecule),
hence W=N!/(N!VS^N)=(1/VS)^N
Now substituting VS=V/N-U1B1mS1U1B0, we get:
W=N!(N-U1B1mS1U1B0 N)N/2 .... 1/(V/N-U1B1mS1U1B0)^N
which is a number with a leading digit 5, so the correct answer is (D).

For a Gas of N Identical Molecules of Molecular Volume