Lessons 9–10 · 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
10
The isothermal process
Textbook: pp. 33–34
GoalKnow the idea of an isoprocess; know and apply the isothermal process and the Boyle–Mariotte law; describe an isotherm.
New words
isoprocess · izojarayonisothermal process · izotermik jarayonBoyle–Mariotte law · Boyl–Mariott qonuniisotherm · izoterma
Explanation
A process in which, for a fixed mass of gas, one of the three parameters is constant while the other two change is called an isoprocess; there are three kinds – isothermal, isobaric and isochoric. A change of state of a gas of constant mass at constant temperature is an isothermal process. It was discovered independently by R. Boyle (1662) and E. Mariotte (1676). The law: at constant temperature the pressure of a given mass of gas is inversely proportional to its volume, i.e. pV = const or p₁V₁ = p₂V₂. For density, ρ₂/ρ₁ = p₂/p₁: if the pressure rises, the density rises by the same factor. On a p–V graph an isothermal process is a hyperbola, the isotherm; a higher temperature puts the isotherm farther from the axes. To keep T constant the gas is compressed or expanded slowly or kept in a thermostat.
Worked examples
12 l of gas is at 100 kPa. Compressed isothermally to 4 l, p₂ = p₁V₁/V₂ = 100·12/4 = 300 kPa.
At the surface (p₁ = 10⁵ Pa) a flexible bag holds 6 l of air. A diver takes it down to a depth of 20 m: p₂ = p₀ + ρgh = 10⁵ + 1000·10·20 = 3·10⁵ Pa (g ≈ 10 m/s²). At the same temperature V₂ = p₁V₁/p₂ = 10⁵·6/(3·10⁵) = 2 l: the bag shrinks 3 times.
Class activity
With a syringe without a needle (with a teacher’s or adult’s help) draw in air, close the tip with a finger and press the piston slowly: how does the pressure (resistance) change as the volume decreases? No needle is used; do not work with sharp objects.
Practice
1
State the Boyle–Mariotte law and write its formula.
At constant temperature and mass, gas pressure is inversely proportional to volume: p₁V₁ = p₂V₂.
2
3 l of gas at 400 kPa expands isothermally to 12 l. What is the new pressure in kPa?
100
3
If a gas’s volume decreases 4 times isothermally, how do pressure and density change?
Both rise 4 times.
4
When pumping air into a tyre the pump warms up, yet the Boyle–Mariotte law says “constant temperature”. Why?
Fast compression changes the temperature; the law holds only for slow compression when the gas stays in thermal equilibrium with its surroundings.