A cubical box, 3 cm to the side, holds 3000 molecules, each with a mass of 10 25

Question

A cubical box, 3 cm to the side, holds 3000 molecules, each with a mass of 1025 kg. The molecules move back and forth in the x direction with speeds of 5000 m/s.

(a) What is the magnitude of the momentum of each molecule?
( )kg m/s

(b) What is the change of momentum when a molecule hits a wall?
( ) kg m/s

(c) What is the time between collisions of a molecule with one wall?
( ) s

(d) What is the average force on one of the walls perpendicular to the x direction?

(e) What is the pressure?
( ) N/m^2

Explanation / Answer

A) momentum p = m*v = 10^-25*5000 = 5*10^-22 kg m/s

B) change of momentum is dp = 2*m*v = 2*5*10^-22 = 10^-21 kg m/s

C) time t = distance/ speed = 0.03/5000 = 6*10^-6 Sec

D) Favg*dt = change in momentum = 10^-21

one moelecule

Favg = 10^-21/(6*10^-6) = 1.67*10^-16 N

3000 molecules

Favg = 1.67*10^-16*3000 = 5*10^-13 N

E) Pressure P = F/A = (5*10^-13)/(0.03*0.03) = 5.55*10^-10 N/m^2

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