Question

Question involving thermal behaviour of matter:

A pressure of 10^-10 Pa is readily achievable with laboratory vacuum apparatus.
a) If the residual air in this vacuum is at 0°C, how many airmolecules are in 1 L? (Wolfson, University fysics question 22 chapter 17)
b) What is the thermal speed v_th of these molecules (extra question, not in the book)

Thank you!

Answer 1

Step 1 of 5

For a given pressure with laboratory vaccum apparatis, we need to find,

(a) How many air molecules are present in 1 litre of air in the vaccum at

(b) What is the thermal speed of these molecules.

Step 2 of 5

(a)

Given,

Let us consider the ideas gal equation given by,

....(1)

where,

....(2)

where, is the Boltzmann constant =

N - number of gas molecules

P - absolute pressure in Pa

V - volume in

Step 3 of 5

Now, from eq(2) we have,

....(3)

on substituting the values we get,

Hence, the number of air molecules present in 1Litre is

Step 4 of 5

(b)

To find the thermal speed of the air molecules, let us consider the equation of thermal speed given by,

....(4)

where, M is the molecular mass of air ,

  

Step 5 of 5

on substituting the values in eq(4) we get,

Hence, the thermal speed of these molecules is, 484.89 m/s