CAIE A-Level Physics 15.3.3 Root-Mean-Square Molecular Speed

Practise interpreting r.m.s. molecular speed, relating mean-square speed to molecular motion, temperature, mass and kinetic-theory quantities.

Exam points

calculate or interpret root-mean-square speed from the mean-square molecular speed
relate c_rms to molecular motion, temperature or the quantities in the kinetic-theory equations

[Maximum number: 3]

A sealed vessel contains a mass of 0.0424 kg of an ideal gas at $227^{\circ} \mathrm{C}$ . The pressure of the gas is $1.37 \times 10^{5} \mathrm{~Pa}$ and the volume of the gas is $0.640 \mathrm{~m}^{3}$ .

Calculate:

the root-mean-square (r.m.s.) speed v of the molecules of the gas.

\begin{aligned} & v= \\ & \mathrm{ms}^{-1} \end{aligned}

$\frac{1}{2} m\left\langle c^{2}\right\rangle=(3 / 2) k T$

C1

$3.34 \times 10^{-27} \times v^{2}=3 \times 1.38 \times 10^{-23} \times 500$

C1

$v=2490 \mathrm{~m} \mathrm{~s}^{-1}$

A1

or

$p V=1 / 3(N m)\left\langle c^{2}\right\rangle$ and N m= mass of gas

(C1)

$0.0424 \times v^{2}=3 \times 1.37 \times 10^{5} \times 0.640$

(C1)

$v=2490 \mathrm{~m} \mathrm{~s}^{-1}$

(A1)

All question bank results loaded

15.3.3—The root-mean-square speed cr.m.s. is given by c<>2 question 1