☰ Contents · Physics

First-law problems and the second law

Lessons 24–25 · 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
24

Problem solving

Textbook: pp. 70–71
GoalApply the first law of thermodynamics to problems on isoprocesses.
New words
signs of Q, ΔU and A · Q, ΔU va A ishoralarimonatomic gas · bir atomli gazisobaric heat · izobarik issiqlikfunction of state · holat funksiyasi
Explanation

In problems first identify the process and adapt Q = ΔU + A to it. Isochoric: A = 0, Q = ΔU = (3/2)νRΔT. Isothermal: ΔU = 0, Q = A. Adiabatic: Q = 0, ΔU = –A. For a monatomic gas isobarically: A = pΔV = νRΔT, ΔU = (3/2)pΔV, Q = (5/2)pΔV, so A = 0.4Q and ΔU = 0.6Q. Signs: Q > 0 if the gas receives heat, Q < 0 if it gives it off; A > 0 when the gas expands, A < 0 when compressed; ΔU > 0 when the gas warms. The change of internal energy depends only on the initial and final states, not on the path, but Q and A depend on the path. Use SI units and check the sign of the result.

Worked examples
A monatomic gas expands isobarically by 0.02 m³ at 100 kPa: A = pΔV = 2000 J; ΔU = 1.5·2000 = 3000 J; Q = ΔU + A = 5000 J.
2 mol of a monatomic gas in a steel cylinder is heated by 30 K (isochoric): A = 0, Q = ΔU = 1.5·2·8.31·30 ≈ 748 J.
Class activity

“Q, ΔU, A” table: on the board draw 4 rows (isothermal, isobaric, isochoric, adiabatic) and three columns; groups fill each cell with “+”, “–” or “0” for expansion and heating. Then check with another group.

Practice
1
A monatomic gas does 600 J of work in isobaric expansion. How many joules of heat Q was supplied?
2
4 mol of monatomic gas in a sealed vessel is cooled by 50 K. About how much heat does the gas give off?
3
A gas is compressed isothermally: A = –300 J. What is Q and in which direction?
4
When air escapes from a tyre the valve gets cold. Why?