☰ Contents · Physics

Internal energy and thermodynamic work

Lessons 16–17 · 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
16

Internal energy

Textbook: pp. 50–52
GoalUnderstand internal energy; calculate the internal energy of a monatomic ideal gas by U = (3/2)νRT = (3/2)pV.
New words
thermodynamics · termodinamikainternal energy · ichki energiyamonatomic gas · bir atomli gazchange of internal energy · ichki energiyaning o‘zgarishi
Explanation

Thermodynamics studies the transformation of energy from one kind to another in macroscopic systems and pays no special attention to the molecular structure. The sum of the kinetic and potential energies of all particles of a body is its internal energy, U = E_k + E_p. The molecules of an ideal gas do not interact, so the potential energy is zero and the internal energy is the sum of the kinetic energies of all the molecules: U = N·(3/2)kT. Hence for a monatomic ideal gas U = (3/2)(m/M)RT = (3/2)νRT, and by the equation of state U = (3/2)pV. So the internal energy of a given amount of ideal gas depends only on temperature, and its change is ΔU = (3/2)νRΔT. Internal energy also changes when a liquid becomes a gas or a solid becomes a liquid: it rises on melting and falls on solidifying.

Worked examples
2 mol of helium at 300 K: U = (3/2)νRT = 1.5·2·8.31·300 ≈ 7.5·10³ J = 7.5 kJ.
A monatomic gas occupies 0.06 m³ at 100 kPa. U = (3/2)pV = 1.5·10⁵·0.06 = 9000 J = 9 kJ.
Class activity

Card game with three cards: “internal energy rises / falls / unchanged”. The teacher names a situation (ice melting, gas cooling, gas expanding isothermally); groups raise the matching card and give the reason in one sentence.

Practice
1
What is internal energy and what is it made of?
2
4 mol of monatomic gas is cooled by 50 K. How does its internal energy change (approximately)?
3
What is the internal energy (J) of a monatomic ideal gas with p = 200 kPa and V = 0.03 m³?
4
Why does the internal energy of an ideal gas not depend on volume (at constant T)?