☰ Contents · Physics

Practical work and problems

Lessons 13–14 · 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
14

Problem solving

Textbook: pp. 40–43
GoalSolve Chapter I problems on gas laws, the equation of state, density and concentration.
New words
gas law · gaz qonunitype of process · jarayon turidensity · zichlikproblem analysis · masala tahlili
Explanation

To solve a gas problem, first identify the process: if the mass is constant and one parameter is constant, use the matching law (Boyle–Mariotte, Gay-Lussac or Charles); if all three parameters change, use the Clapeyron equation p₁V₁/T₁ = p₂V₂/T₂. If a mass or an amount of substance is asked for, use the Mendeleev–Clapeyron equation pV = (m/M)RT. Density follows from ρ = pM/(RT), and for two states ρ₂/ρ₁ = (p₂/p₁)(T₁/T₂). Temperature must be in kelvins; for p and V used in ratios it is enough that the units are the same (kPa, l). Check the result with physical sense (compression raises pressure, heating expands).

Worked examples
A gas has density 1.8 kg/m³ at 27 °C and 150 kPa. At 127 °C and 100 kPa the density is ρ₂ = ρ₁(p₂/p₁)(T₁/T₂) = 1.8·(100/150)·(300/400) = 0.9 kg/m³.
A bicycle tyre has volume 2000 cm³ and contains air at 100 kPa. Each pump stroke adds 200 cm³ of air at 100 kPa. After 10 strokes (same temperature) p₂ = 100·(2000 + 10·200)/2000 = 200 kPa.
Class activity

“Which law?” game: the teacher reads a problem (without calculating); within a minute groups name the process, the law and the formula. Correct answers score points.

Practice
1
A gas of constant volume has pressure 250 kPa and its temperature rises from 300 K to 360 K. What is the new pressure in kPa?
2
A 8.31 l vessel contains nitrogen (M = 28 g/mol) at 300 K and 300 kPa. What is its mass in grams?
3
A gas was first heated isochorically and then expanded isothermally. How did the pressure change in each stage?
4
Why is temperature entered in kelvins and not Celsius in gas problems, while p and V can stay in kPa and l when used in ratios?