Specific Heat of Metals Lab Experiment
This experiment was conducted to identify a quantity of unknown metal using calorimeter and conservation of heat principles and determine specific heat of metals.
Specific Heat of Metal by definition: The heat required to raise the temperature of the unit mass of a given substance by a given amount (usually one degree).
Credit for the concept of specific heat usually goes to the Scottish chemist Joseph Black. In the 18th century he noticed that equal masses of different substances need different amounts of heat to raise them through the same temperature interval, and from that observation he founded the concept of specific heat (Britannica); accounts of his work date the insight to around 1760. The Swedish physicist Johan Carl Wilcke also worked on the idea and published his own measurements of specific heats in 1781; the term “specific heat” itself first appeared in print in 1780, in a book by J. H. de Magellan. William Cleghorn, a student of Black’s, is remembered instead for his 1779 Edinburgh dissertation De igne, which set out rules for the caloric theory of heat that were used to explain heat conduction and specific heats (John H. Lienhard, New York Academy of Sciences). Black is also known for the concept of latent heat — the heat taken in when a solid melts or a liquid boils without any change in temperature.
| Density Table | |||
| Trial 1 | Trial 2 | ||
| Initial Height (cm) |
13.1 |
20.8 |
|
| Final Height (cm) |
13.2 |
21 |
|
| Change (cm) |
0.2 |
0.2 |
|
| Volume (cm3) |
5.67 |
5.67 |
|
| Density (g/cm3) |
11.2 |
11.1 |
|
| Density Table | |||
| Trial 1 | Trial 2 | Trial 3 | |
| Mass (g) |
15.4 |
6.5 |
9.7 |
| Radius (cm) |
0.725 |
0.53 |
|
| Volume (cm3) |
1.596 |
0.097 |
1.12 |
| Density (g/cm3) |
9.64 |
9.33 |
8.67 |
| Specific Heat Calculations | Trial 1 | Trial 2 | |
| Mass Inner Cup (g) |
53.5 |
53.6 |
|
| Mass of Metal (g) |
63.4 |
63.15 |
|
| Mass of Calorimeter Cup (g) |
27.15 |
27.15 |
|
| Mass of Water (g) |
113.05 |
114.2 |
|
| Tm, metal initial (°C) |
98.3 |
97.2 |
|
| Tw, water initial (°C) |
16.2 |
15 |
|
| Tf, final (°C) |
20.8 |
19.4 |
|
How the calorimetry calculation works
The method rests on conservation of energy: the heat lost by the hot metal equals the heat gained by the cooler water (assuming no heat escapes to the surroundings), so qmetal = −qwater. Each heat term is found from q = c × m × ΔT, where c is specific heat, m is mass and ΔT is final minus initial temperature. Source: OpenStax Chemistry 2e, 5.2 Calorimetry, which identifies an unknown metal the same way in its Example 5.4.
Worked example with Trial 1 data from the table above (water only, cwater = 4.184 J/g·°C):
- Heat gained by the water: qwater = 4.184 × 113.05 g × (20.8 − 16.2) °C ≈ 2,176 J
- Temperature change of the metal: 20.8 − 98.3 = −77.5 °C
- Specific heat of the metal: cmetal = 2,176 J / (63.4 g × 77.5 °C) ≈ 0.443 J/g·°C, or about 443 J/kg·K
This simplified estimate ignores the heat taken up by the calorimeter cup and any heat lost to the room, so it will not exactly match the report’s final value of 459 J/kg·K; the report does not reprint every step of its own calculation. Either way, the result sits close to nickel’s accepted value of 444 J/kg·K. For another example of the same heat-balance method, see Identifying Unknown Salts with Calorimetry.
Conclusion
The sample has been identified as nickel, with an experimental specific heat of 459 (J/kg.K). The experimental value has 3.38% error when compared to the accepted value of 444 (J/kg.K). Error is mostly due to heat loss in surroundings and variations in actual specific heats.