Heat Capacity Calculator

Q = m * c * deltaT expresses the sensible heat associated with a temperature change, distinct from latent heat, which flows during a phase change at constant temperature. Specific heat capacity c is intensive, a property of the material, while the product m*c is the extensive heat capacity of the particular object in J per degree C. Representative values in J per g per degree C are 4.186 for liquid water, 2.09 for ice, 2.03 for steam, 0.897 for aluminum, 0.449 for iron, 0.385 for copper and 0.129 for lead. Water is the outlier because much of the added energy disrupts its hydrogen bond network rather than raising molecular kinetic energy, which makes it an effective coolant and gives oceans their moderating influence on coastal climate. The inverse relation between specific heat and atomic mass is not accidental: the Dulong-Petit rule holds that molar heat capacity approaches 3R, near 25 J per mol per K, for most crystalline elements at room temperature, so heavy elements have small specific heats per gram. In practice c varies with temperature, falling toward zero near absolute zero, and jumps discontinuously at phase transitions. For gases the distinction between constant pressure and constant volume matters, with Cp minus Cv equal to R per mole for an ideal gas, so using a Cp value in a rigid sealed vessel introduces real error. Calculations that cross a melting or boiling point must add the latent heat separately; ignoring the 334 J/g needed to melt ice or the 2257 J/g to vaporize water is the most common source of large errors.

Joseph Black, lecturing at Glasgow and later Edinburgh in the 1750s and 1760s, drew the distinction that makes this calculation possible: heat and temperature are not the same quantity. By observing that ice absorbs heat while remaining at its melting temperature, and that equal masses of different substances need different amounts of heat for the same temperature rise, he introduced both latent heat and what he called the capacity for heat. Antoine Lavoisier and Pierre-Simon Laplace built an ice calorimeter around 1783 that measured heat by the mass of ice melted, producing the first quantitative capacity data. Pierre Louis Dulong and Alexis Therese Petit reported in 1819 that the product of specific heat and atomic weight is roughly constant across solid elements, a regularity that was used through the nineteenth century to assign atomic weights and that later became a key test case for quantum theory. Classical physics could not explain why heat capacities collapse at low temperature; Albert Einstein addressed this in 1907 with a quantized oscillator model, and Peter Debye refined it in 1912 with the treatment that yields the T cubed dependence observed near absolute zero. Meanwhile James Prescott Joule established the mechanical equivalent of heat through the 1840s, and the calorie was eventually superseded by the joule in SI usage, although the calorie persists in nutrition and parts of engineering practice.