☰ Contents · Physics

The ideal gas and temperature

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
6

Temperature

Textbook: pp. 21–24
GoalConvert between the Celsius and Kelvin scales; know the molecular-kinetic meaning of temperature and the formula p = nkT.
New words
temperature · temperaturaabsolute zero · absolyut nolBoltzmann constant · Bolsman doimiysithermal equilibrium · issiqlik muvozanati
Explanation

Temperature is a quantity describing quantitatively how hot a body is. In thermal equilibrium the temperatures of bodies become equal and heat exchange stops. On the Celsius scale (A. Celsius, 1742) ice melts at 0 °C and water boils at 100 °C (at normal pressure). The absolute scale (Kelvin, 1848) has the unit K, a base SI unit; absolute zero is –273.15 °C ≈ –273 °C, and the conversion is T = t + 273, with ΔT = Δt. From the molecular-kinetic point of view temperature measures the average translational kinetic energy of molecules: E_k = (3/2)·k·T, where k = 1.38·10⁻²³ J/K is the Boltzmann constant. Substituting into p = (2/3)nE_k gives p = nkT: gas pressure is proportional to the concentration and the absolute temperature.

Worked examples
t = 27 °C → T = 27 + 273 = 300 K. T = 400 K → t = 400 – 273 = 127 °C. If the temperature rises from 20 °C to 50 °C, ΔT = Δt = 30 K.
With n = 2.5·10²⁵ m⁻³ and T = 300 K, p = nkT = 2.5·10²⁵·1.38·10⁻²³·300 ≈ 1.0·10⁵ Pa, close to atmospheric pressure. At this temperature E_k = 1.5·1.38·10⁻²³·300 ≈ 6.2·10⁻²¹ J.
Class activity

Thermometer exercise (under teacher supervision): record the reading in room-temperature water, in warm water prepared by the teacher (no hotter than about 40 °C) and in cold water, and convert them to kelvins. Students do not handle hot water.

Practice
1
What is absolute zero and what is it on the Celsius scale?
2
Express 207 °C on the Kelvin scale (K).
3
Express 250 K on the Celsius scale (°C).
4
A gas in a closed vessel is heated from –23 °C to 477 °C. By what factor does the pressure change, and why?