Even when the same amount of heat is supplied, the temperature rises differently depending on the substance. Specific heat and heat capacity describe this difference.
Basic Knowledge
Specific heat c: The amount of heat required to raise the temperature of 1 kg of an object by 1 K (= 1℃). The unit is J/(kg·K).
The specific heat of water is about 4200 J/(kg·K), while that of iron is about 460 J/(kg·K); these values differ by substance.
Heat capacity C: The amount of heat required to raise the temperature of an entire object by 1 K. The unit is J/K.C = mc (mass × specific heat)
Formula for heat quantity:Q = mcΔT = CΔT
Q: heat quantity (J), m: mass (kg), c: specific heat, ΔT: temperature change (K or ℃).
Law of conservation of heat: When objects are mixed in an insulated container,heat lost by the hotter object = heat gained by the colder objectm₁c₁(T₁ - T) = m₂c₂(T - T₂)
Specific heat c（Heat required to raise 1 kg by 1 K. J/(kg·K). A value specific to each substance）
Heat capacity C（Heat required to raise an entire object by 1 K. C = mc, unit: J/K）
Q = mcΔT（Formula for calculating heat quantity）
ΔT（Temperature change. Final temperature - initial temperature）
Law of conservation of heat（When there is no heat exchange with the outside, heat gained = heat lost）
Specific heat of water（About 4200 J/(kg·K). Much greater than that of other substances）
Further Study (Background and Significance)
The high specific heat of water greatly affects Earth's environment. Because the ocean contains a huge amount of water, it stores a large amount of heat and changes temperature slowly. This causes a maritime climate (mild temperatures with small temperature differences). In contrast, deserts, where sand has a low specific heat, have large differences between daytime and nighttime temperatures.
The high specific heat of water also plays an important role in regulating human body temperature. Because much of the body consists of water, body temperature does not change suddenly even when the heat quantity changes slightly.
In mixing problems using the law of conservation of heat, the basic method is to set up “heat lost by the hotter object = heat gained by the colder object.” This calculation requires the condition of an insulated container (no heat exchange with the outside).
- Specific heat: heat required to raise 1 kg by 1 K [J/(kg·K)]
- Heat capacity C = mc (heat capacity of the entire object)
- Q = mcΔT = CΔT
- Specific heat of water: 4200 J/(kg·K) (large)
- Mixing: heat lost by the hotter object = heat gained by the colder object
- ΔT is the amount of change (final - initial)
- A larger specific heat means harder to heat and harder to cool
Important Notes (Common Confusions)
① Do not confuse specific heat (per unit mass) with heat capacity (the entire object). “A larger specific heat means a larger specific heat capacity” is correct, but “a larger heat capacity means a larger specific heat” is not necessarily correct because mass is involved. ② ΔT is final - initial. It is negative when an object cools. ③ Mixing problems assume an insulated container. ④ Temperature change ΔT has the same numerical value in ℃ and K because it is a difference. Either may be used in calculations.
Practice
- Find the heat required to heat 2 kg of water (specific heat 4200 J/(kg·K)) from 20℃ to 70℃.
- Find the heat capacity of 0.5 kg of iron (specific heat 460 J/(kg·K)).
- 0.2 kg of water at 100℃ was mixed with 0.3 kg of water at 20℃. Find the temperature after mixing (the specific heats of water are equal and can therefore be canceled).