CAIE A-Level Physics A2 15.3.2 How Molecular Movement Causes the Pressure Exerted By a Gas and Derive and

[Maximum number: 4]

(a)

A molecule of an ideal gas has mass m and is contained in a cubic box of side length L. The molecule is moving with velocity u towards the face of the box that is shaded in Fig. 3.1.

Fig. 3.1

The molecule collides elastically with the shaded face and the face opposite to it alternately.
Deduce expressions, in terms of m, u and L, for:

[ 4 ]

(i)

the magnitude of the change in momentum of the molecule on colliding with a face

change in momentum =

[ 1 ]

(ii)

the time between consecutive collisions of the molecule with the shaded face
time =

[ 1 ]

(iii)

the average force exerted by the molecule on the shaded face

force =

[ 1 ]

force = change in momentum / time = 2 m u /(2 L / u)
$=m u^{2} / L$

(iv)

the pressure on the shaded face if the force in (iii) is exerted over the whole area of the face.

pressure =

[ 1 ]

$\begin{aligned} \text { pressure } =\text { force } / \text { area }=\left(m u^{2} / L\right) / L^{2} =m u^{2} / L^{3} \end{aligned}$

CAIE A-Level Physics A2 15.3.2 How Molecular Movement Causes the Pressure Exerted By a Gas and Derive and Topic Practice

Question 1

Question (a)

Question (i)

Question (ii)

Question (iii)

Question (iv)