Lessons 5–6 · 2 lessons · P. Habibullayev, A. Boydedayev, A. Bahromov, K. Suyarov, J. Usarov, M. Yuldasheva. Physics Grade 9, revised and expanded 3rd edition. G‘afur G‘ulom Publishing House, Tashkent, 2019
5
The ideal gas
Textbook: pp. 18–20
GoalKnow the difference between ideal and real gas; explain the cause of gas pressure and use the basic equation of MKT.
New words
ideal gas · ideal gazreal gas · real gazroot-mean-square speed · o‘rtacha kvadratik tezlikgas pressure · gaz bosimi
Explanation
In a rarefied gas the distance between molecules is much greater than their size, so molecules can be treated as material points and their interaction ignored. A gas whose molecules are material points and do not interact is an ideal gas; a gas whose properties depend on the interaction of its molecules is a real gas. Gas pressure on a vessel wall is caused not by one molecule but by the almost continuous impacts of a huge number of molecules; at each impact a molecule gives the wall an impulse. The pressure depends on the concentration n, the mass of one molecule m₀ and the root-mean-square speed v: p = (1/3)·n·m₀·v² (the basic equation of MKT). Since E_k = m₀v²/2 and ρ = n·m₀, the forms p = (2/3)·n·E_k and p = (1/3)·ρ·v² follow as well.
Worked examples
A gas has density ρ = 3 kg/m³ and root-mean-square speed 300 m/s. Pressure: p = (1/3)ρv² = (1/3)·3·300² = 90 000 Pa = 90 kPa.
If p = 150 kPa and n = 2.5·10²⁵ m⁻³, the average translational kinetic energy of a molecule is E_k = 3p/(2n) = 3·1.5·10⁵ / (2·2.5·10²⁵) = 9·10⁻²¹ J.
Class activity
Safe model: put small dry peas in a cardboard box and shake it gently, feeling the impacts on the lid (card). How do the impacts change when you add more peas? Use only dry peas and a cardboard box.
Practice
1
What kind of gas is called an ideal gas?
A gas whose molecules are treated as material points and whose mutual forces are neglected.
2
If ρ = 2 kg/m³ and v = 300 m/s, what is the gas pressure (Pa)?
60000
3
Find the root-mean-square speed of molecules in a gas with p = 90 kPa and ρ = 3 kg/m³.
300 m/s
4
If a gas is compressed at constant temperature so that its volume halves, why does the pressure rise (by MKT)?
The concentration n doubles, so molecules hit the wall twice as often; p ∝ n.