An ideal gas at a pressure of $$$1.6 \times 10^{5} \mathrm{~Pa}$$$ has a density of $$$1.9 \mathrm{~kg} \mathrm{~m}^{-3}$$$. (i) Show that the root-mean-square (r.m.s.) speed of molecules of this gas is approximately $$$500 \mathrm{~ms}^{-1}$$$. (ii) One molecule of the gas has a mass of $$$4.7 \times 10^{-26} \mathrm{~kg}$$$. Determine the thermodynamic temperature of the gas. temperature = K

Physics

IGCSE&ALevel

CAIE

Exam No：9702_s25_qp_44 Year：2025 Question No：3(b)

Answer:

Knowledge points:

15.2.1 recall and solve problems using the equation of state for an ideal gas expressed as pV = nRT, where n = amount of substance (number of moles)

15.3.1 infer from a brownian motion experiment the evidence for the movement of molecules

15.3.2 state the basic assumptions of the kinetic theory of gases

15.3.3 explain how molecular movement causes the pressure exerted by a gas and hence deduce the relationship Nm c2 , where N = number of molecules [a simple model considering one-dimensional collisions and then extending to three dimensions using is sufficient.

Answer:

Knowledge points:

Solution:

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