☰ Contents · Physics

Isobaric and isochoric processes

Lessons 11–12 · 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
12

The isochoric process

Textbook: p. 37
GoalKnow and apply the isochoric process and Charles’s law; describe an isochore.
New words
isochoric process · izoxorik jarayonCharles’s law · Sharl qonuniisochore · izoxorasealed vessel · germetik idish
Explanation

A change of state of a gas at constant mass and volume is called an isochoric process (“choros” means volume). Dividing the equations of state for two states with V = const gives p₁/T₁ = p₂/T₂. This is the law found experimentally by J. Charles in 1787: at constant volume the ratio of the pressure of a given mass of gas to its absolute temperature is constant, i.e. p ∝ T. (Many English-language textbooks swap the two names, calling V ∝ T “Charles’s law” and p ∝ T “Gay-Lussac’s law”.) On a p–T graph an isochore is a straight line through the origin. In MKT the cause is that a heated gas has faster molecules that hit the wall harder and more often, and since the volume is fixed the pressure rises. In an isochoric process the gas does no work because the volume does not change. Heating a gas in a closed container is dangerous: never bring a sealed vessel, aerosol can or gas cylinder near fire.

Worked examples
A closed vessel holds gas at 200 kPa and 27 °C. Heated to 327 °C (300 K → 600 K): p₂ = p₁T₂/T₁ = 200·600/300 = 400 kPa, i.e. it doubles.
A sealed can holds gas at 300 kPa and 27 °C. In a fire it reaches 627 °C (900 K), so p₂ = 300·900/300 = 900 kPa. That is why heating such cans can cause an explosion and they must be kept away from fire.
Class activity

Observation (shown by the teacher only): close a plastic bottle tightly in a cool room, then place it in warm water (not above 40 °C) and show how the walls change. Students do not handle boiling water or fire; heating a closed vessel is forbidden.

Practice
1
State Charles’s law and write its formula.
2
At constant volume the gas pressure fell from 240 kPa to 160 kPa. The initial temperature was 300 K. What is the new T in K?
3
What does an isochore graph look like?
4
Why does the pressure of gas in a closed vessel rise when it is heated? Explain by MKT.