Question

The canonical ensemble partition function Q for a mixture of two monatomic ideal gases is given by

Q= q1^N1/N1! * q2^N2/N2!

SHOW THAT U=3/2(n1+n2)RT

AND PV=(n1+n2)RT

Answer 1

Consider a cube of dimension xx in space There are N particles in our - system. - For the sake of mathematical we consider that the randon particks is exactly / per simplicity nation of direction. the Consider single any one particle with normal mass in direction and one and velocity v. - I mu i l lo Now, the force exerted by the single particle on the right side fac é is the rate of change of momentum oirer time. - a. Info API Min fact ILE AP . For a pefectly elastic collistes, P2-2. my-(-mu 2mv 19E st New Ati Distanie travelled a Velocity Fa 2mV my? 2xhxx - . Pressure exerted by one particle on one face is

Puf mx stop__oris gan P. mv²ton t Volume of system. - Total pressure exerted by a porticles on His right face is a solutions 2479x Dj pasmVSN 3.PH. NAV? 2 3 Pu= N( I mu Now NMJ² : KE ct system -,99 Com plemente de ternal Energy 3 pu: US . U= 3 PUT EART MRT (By ideal gas law) If total no. of moles n= nith TU=(n + Me) RT