Question

If 10²⁰ oxygen molecules per second strike 4 cm² of wall at an angle of 30° with the normal when moving at a speed of 2 × 10³ ms⁻¹, find the pressure exerted on the wall. (mass of one oxygen atom = 2.67 × 10⁻²⁶ kg)

Answer 1

Mass of O₂ atom = 16 × mass of 1 atom

= 16 × 10²⁰ × 2.67 × 10⁻²⁶

m = 42.72 × 10⁻⁶ kg

Momentum of the O₂ molecule (P) = mv = 42.72 × 10⁻⁶ × 2 × 10³

P = 85.44 × 10⁻³ kg ms⁻¹

 Momentum normal to the wall at angle 30°

= 85.44 × 10⁻³ × cos 30°

= 73.99104 × 10⁻³ kg ms⁻¹

Pressure = `"F"/"A" = "Change in momentum"/"Area"`

= `(73.99104 xx 10^-3)/((4 xx 10^-2)^2)`

= `(73.99104 xx 10^-3 xx 10^4)/16`

= 4.62444 × 10

P = 46.2 Nm⁻²