☰ Contents · Physics

Quantity of heat

Lessons 18–19 · 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
19

Problem solving

Textbook: pp. 60–62
GoalSolve problems on heat, heat balance, work and internal energy.
New words
conservation of energy · energiyaning saqlanishitemperature of a mixture · aralashma temperaturasiisobaric heating · izobarik qizdirishheat loss · issiqlik yo‘qotishi
Explanation

In heat problems first list the bodies and their initial temperatures. Decide which gives up heat (cools) and which receives it (warms), set up the balance Q_given = Q_received, and use mass and c in consistent units. If mechanical energy turns into heat, e.g. a body falling from a height and hitting the ground, mgh = cmΔt gives Δt = gh/c. In gas problems the change of internal energy ΔU = (3/2)νRΔT (monatomic gas) and the isobaric work A = νRΔT are found separately; ΔU depends only on the initial and final states, not on the path the gas took. Check the result: the temperature of a mixture must lie between the initial temperatures.

Worked examples
A lead ball (c = 130 J/(kg·K)) falls 26 m and hits the ground. If all the energy heats the ball (g ≈ 10 m/s²): Δt = gh/c = 10·26/130 = 2 K. The answer does not depend on the mass.
1.5 mol of monatomic gas is heated isobarically by 40 K: ΔU = (3/2)νRΔT = 1.5·1.5·8.31·40 ≈ 748 J; the work done by the gas A = νRΔT = 1.5·8.31·40 ≈ 499 J. Note that A/ΔU = 2/3.
Class activity

Class game “Balance”: two cards give masses and temperatures of water; the group guesses the final temperature (before calculating), then calculates and compares. Calculation only; no boiling water is used.

Practice
1
How much heat (J) is needed to heat 3 kg of water from 10 °C to 60 °C? c = 4200 J/(kg·K).
2
2 kg of water at 90 °C is mixed with 6 kg of water at 10 °C. What is the final temperature in °C?
3
A monatomic gas is heated isobarically and its internal energy rises by 600 J. How much work does it do (J)?
4
Why do heat-balance problems assume “no heat is lost to the surroundings”, and how does this affect a real experiment?