Mixing Hot & Cold
Pour hot water into cold, or drop a hot piece of metal into water: both end up at the same temperature. Find that final temperature — or measure it, and work out the specific heat of an unknown material.
How Mixing Works
When a hot and a cold object touch, heat flows from hot to cold until both have the same temperature. If no heat escapes, the heat the hot one loses is exactly the heat the cold one gains. The final temperature is a weighted average, weighted by each object’s heat capacity m·c.
That is why a hot iron nail hardly warms a glass of water: water has a large heat capacity. Turned around, the temperature rise of the water tells you the specific heat of the nail — this is calorimetry.
Heat Balance
TₗA Hot Sample into Water
100 g at 100 °C into 200 g at 20 °C| Object dropped in | c, J/(g·K) | Final temperature |
|---|---|---|
| Water | 4.184 | 46.7 °C |
| Aluminium | 0.900 | 27.8 °C |
| Iron | 0.449 | 24.1 °C |
| Copper | 0.385 | 23.5 °C |
Worked Techniques
Heat lost by the hot part equals heat gained by the cold part. For two amounts of water, c cancels and Tf is the mass-weighted average.
Heat a sample in boiling water, drop it into a cup of cold water and read the final temperature. Compare the result with known specific heats.
Rearranged for water only, the heat balance tells you how much hot water to add for a given temperature.
Sources & Verification
- S. S. Zumdahl & S. A. Zumdahl, Chemistry, 10th ed., Cengage, 2018 — Ch. 6 (Thermochemistry: enthalpy and calorimetry).
- D. Halliday, R. Resnick & J. Walker, Fundamentals of Physics, 10th ed., Wiley, 2014 — Ch. 18 (Temperature, Heat, and the First Law of Thermodynamics).