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Thermal equilibrium and determining specific heat capacity

Lessons 20–21 · 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
21

Laboratory work: determining the specific heat capacity of a solid

Textbook: p. 64
GoalDetermine the specific heat capacity of a solid with a calorimeter; know the procedure and the sources of error.
New words
calorimeter · kalorimetrmeasurement error · o‘lchash xatoligiheat loss · issiqlik yo‘qotishimean value · o‘rtacha qiymat
Explanation

Aim: find the specific heat capacity c of a metal body. Equipment: calorimeter and stirrer (aluminium, c_k = 890 J/(kg·K)), balance, thermometer, three bodies of the same material, measuring cylinder, hot water. Procedure: 1) weigh the calorimeter and stirrer to find m_k; 2) pour cold water of mass m_s into the calorimeter and measure t₁; 3) weigh the body to find m; 4) the teacher heats the body on a string in hot water and measures its temperature t₂; 5) quickly transfer the body into the calorimeter, stir, and record the highest temperature t of the mixture. Heat balance cm(t₂ – t) = (c_k m_k + c_s m_s)(t – t₁) gives c = (c_k m_k + c_s m_s)(t – t₁) / [m(t₂ – t)]. Repeat for three bodies and take the mean. Only the teacher or a senior helper handles hot water and hot bodies; use tongs and never touch them by hand.

Worked examples
Sample: m_k = 0.05 kg, m_s = 0.2 kg, t₁ = 20 °C, m = 0.1 kg, t₂ = 100 °C, t = 24 °C. Bracket: 890·0.05 + 4200·0.2 = 884.5 J/K. c = 884.5·4 / (0.1·76) ≈ 466 J/(kg·K), close to the table value 460 for steel.
Relative error: (466 – 460)/460 ≈ 0.013, i.e. about 1 %. The error mostly comes from heat lost while transferring the body and the uncertainty of reading the thermometer.
Class activity

Results table: write c₁, c₂, c₃ and the mean for the three bodies, compare with the table, and guess the material (steel 460, copper 390, aluminium 890). After the work let everything cool and hand it to the teacher.

Practice
1
Write the formula for finding c in this work.
2
In a calorimeter 0.2 kg of water warms from 20 °C to 24 °C. How many joules of heat does the water receive?
3
The table gives c = 460 and the measured c = 466 J/(kg·K). About what percent is the relative error?
4
If the body cools while being transferred, is the calculated c larger or smaller than the true value? Why?