Twenty particlcs, each of mass m are confined to a volume V, have the following

Question

Twenty particlcs, each of mass m are confined to a volume V, have the following speeds: two have speed upsilon, three have speed 2 upsilon, five have speed 3 upsilon, four have speed 4 upsilon, three have speed 5 upsilon, two have speed 6 upsilon, and one has speed 7 upsilon. Find the average speed. 3.5 upsilon 3.4u psilon 3.6 upsilon 3.7 upsilon3.65 upsilon Find the more probable speed. upsilonmp =5 upsilon upsilonmp = upsilon upsilonmp=2 upsilon upsilonmp=7 upsilon upsilon=3 upsilon Find the pressure they exert on the walls of the vessel. P=97.5 (mupsilon^2/v) P=89(m upsilon^2/V) p=106.3(m upsilon^2/V) p=90 (m upsilon^2/V) Find the average kinetic energy per particle. K = 5.7 m upsilon^2 K = 6.98 m upsilon^2 K = 7.98 mupsilon^2K = 7.9 m upsilon^2 K = 4.8 m upsilon^2

Explanation / Answer

a) vave=[2(v) + 3(2v) +5(3v)+4(4v)+ 3(5v)+2(6v)+1(7v)]/20=3.65v

(b)

vrms=root {[2(v)2 + 3(2v)2 ++5(3v)^2+4(4v)^2+ 3(5v)^2+2(6v)^2+1( 7v)^]/20} =3.99v;

(c) vmp=3v

(d) PV=(2N/3)(mvrms2/2)

     P=106.3mv2/V

(e) Kave=(mvrms2/2)= 7.98mv2;

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