5. Specific Heat Capacity, Latent Heat and Calorimetry

5.1 Heat Capacity and Specific Heat Capacity

The heat capacity of a body is the amount of heat energy required to raise its temperature by 1°C (or 1 K); it depends on the mass and the nature of the material of the body. Specific heat capacity (denoted c or s) is a more fundamental, material-specific property: it is defined as the amount of heat energy required to raise the temperature of unit mass (1 kg, or 1 g) of a substance by 1°C (or 1 K). It is measured in J/(kg·K) in SI units, or historically in cal/(g·°C). The specific heat capacity of water is unusually high: 4186 J/(kg·K), equivalently 1 cal/(g·°C) by the original definition of the calorie. This means water needs to absorb (or release) a comparatively large amount of heat energy to change its temperature by even one degree, compared to most other common substances.

The heat energy Q required to change the temperature of a body of mass m, made of a substance of specific heat capacity c, by an amount ΔT (change in temperature) is given by the fundamental calorimetric formula: Q = m × c × ΔT. This single formula underlies almost all quantitative problems on specific heat and calorimetry asked in competitive exams.

Why Water's High Specific Heat Matters

Because water has such a high specific heat capacity compared to land and rock, large water bodies (oceans, seas, and lakes) heat up and cool down much more slowly than the adjoining land masses under the same solar heating. This is the fundamental reason behind several important geographical phenomena tested in general science and geography sections: the moderate, equable climate of coastal regions compared to the extreme climate of continental interior regions at similar latitudes; the daily land and sea breeze cycle; and the seasonal monsoon wind reversal over the Indian subcontinent, which is driven in large part by the differential heating and cooling rates of the Indian Ocean/Arabian Sea/Bay of Bengal versus the Asian landmass. Water is also used as an effective coolant in car radiators and industrial cooling systems precisely because it can absorb large quantities of heat with only a modest rise in its own temperature.

5.2 Latent Heat

When a substance is heated, its temperature does not always rise steadily — during a change of physical state (phase change), such as melting or boiling, the temperature of the substance remains constant even though heat continues to be supplied. This 'hidden' heat, which is used entirely to break the intermolecular bonds and change the state of the substance rather than to raise its temperature, is called latent heat (from Latin latere, 'to lie hidden'). Latent heat is defined as the amount of heat required to change the state of unit mass of a substance, at constant temperature, without any change in temperature. It is measured in J/kg.

There are two principal types of latent heat relevant to solid–liquid–gas transitions:

• Latent heat of fusion (Lf): the amount of heat required to convert unit mass of a solid completely into liquid at its melting point, without any change in temperature. For ice, the latent heat of fusion is approximately 3.34 × 10⁵ J/kg (334 J/g, or about 80 cal/g). The same amount of heat is released when unit mass of the liquid solidifies (freezes) back into a solid at the same temperature.
• Latent heat of vaporisation (Lv): the amount of heat required to convert unit mass of a liquid completely into vapour (gas) at its boiling point, without any change in temperature. For water, the latent heat of vaporisation is approximately 22.6 × 10⁵ J/kg (2260 J/g, or about 540 cal/g). The same amount of heat is released when unit mass of the vapour condenses back into liquid at the same temperature.

The total heat required for a phase change of a mass m of substance is: Q = m × L (where L is the appropriate latent heat, of fusion or vaporisation). It is worth noting that the latent heat of vaporisation of water is much larger than its latent heat of fusion — this is why a steam burn from water vapour at 100°C is far more dangerous and damaging to skin than a burn from boiling water at the same 100°C: the steam releases a much larger quantity of latent heat as it condenses on the skin, in addition to then cooling down as hot water.

5.3 Calorimetry

Calorimetry is the branch of heat measurement concerned with determining quantities of heat, such as the specific heat capacity of an unknown substance, using a device called a calorimeter — typically an insulated vessel (often made of copper, a good conductor, with an outer insulating jacket to prevent heat loss to the surroundings) fitted with a thermometer and a stirrer. The fundamental principle used in calorimetry is the principle of conservation of energy applied to heat exchange, often called the principle of mixtures or the law of heat exchange: when two bodies at different temperatures are placed in contact (or mixed) inside an ideally insulated system with no heat loss to the surroundings, heat lost by the hotter body exactly equals heat gained by the colder body, until both reach a common equilibrium temperature. This is expressed as: Heat lost by hot body = Heat gained by cold body, i.e., m₁c₁(T₁ − Tf) = m₂c₂(Tf − T₂), where T₁ and T₂ are the initial temperatures of the hot and cold bodies respectively and Tf is the final common (equilibrium) temperature. This principle is used routinely to determine the unknown specific heat capacity of a solid or liquid experimentally, by mixing a known mass of it at a known temperature with a known mass of water at a known (different) temperature, measuring the resulting equilibrium temperature, and solving for the unknown specific heat.