A cubical box, 4 cm to the side, holds 2250 molecules, each with a mass of 10 25
ID: 1432141 • Letter: A
Question
A cubical box, 4 cm to the side, holds 2250 molecules, each with a mass of 1025 kg.The molecules move back and forth in the x direction with speeds of 3750 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?
i.one molecule:________N
ii.2250 molecules:______N
(e) What is the pressure? N/m2
Explanation / Answer
a = length of each side of cube = 4 cm = 0.04 m
n = number of molecules = 2250
m = mass of each molecule = 10-25 kg
V = speed of each molecule = 3750 m/s
a)
magnitude of momentum of each molecule = mass x speed = 10-25 x 3750 = 3.75 x 10-22 kgm/s
b)
change of momentum = 2 x 3.75 x 10-22 = 7.5 x 10-22 kgm/s
c)
t = 2 a / V = 2 x 0.04 / 3750 = 2.13 x 10-5 sec
d)
i)
average force = F t = change in momentum
F (2.13 x 10-5 ) = 7.5 x 10-22
F = 3.52 x 10-17 N
ii)
for 2250 molecules
F' = 2250 x 3.52 x 10-17 = 7.92 x 10-14 N
e)
A = area of wall = 0.04 x 0.04 = 16 x 10-4
pressure = F / A = 3.52 x 10-17 / (16 x 10-4 ) = 2.2 x 10-14 N/m2