# Sensible heat

It is common sense that heat flows from an object at a higher temperature to one at a lower temperature. Before the nineteenth century, it was believed that heat was a fluid substance named caloric. The temperature of an object was thought to increase when caloric flowed into an object and to decrease when caloric flowed out of the object. Combustion was believed to be a process during which a large amount of caloric was released. Because heat flow never produced a detectable change in mass, and because caloric could not be detected by any other means, it was logical to assume that caloric was massless, odorless, tasteless, and transparent. Although the caloric theory explained many observations, such as heat flow from an object with a high temperature to one at a lower temperature, it was unable to account for other phenomena, such as heat generated by friction. For example, one can rub together two pieces of metal for a long time and generate heat indefinitely, a process that is inconsistent with a characterization of heat as a substance of finite quantity contained within an object. In the 1800s an English brewer, James Prescott Joule, established our current understanding of heat through a number of experiments. One of his experiments is demonstrated in the figure on the right.

The paddle wheel turns when the weight lowers, and friction between the paddle wheel and the water causes the water temperature to rise. The same temperature rise can also be obtained by heating the water on a stove. From this and many other experiments, Joule found that 4.18 joules (J) of work always equals 1 calorie (cal) of heat, which is well known today as the mechanical equivalent of heat. Therefore heat, like work, is a transfer of thermal energy rather than the flow of a substance. In a process where heat is transferred from a high-temperature object to a low-temperature object, thermal energy, not a substance, is transferred from the former to the latter. In fact, the unit for heat in the SI system is the joule, which is also the unit for work.

The amount of sensible heat Q required to raise the temperature of a system from T2 to T1 is proportional to the mass of the system and the temperature rise, i.e.,

Q = mc(T2T1)

where the proportionality constant c is called the specific heat and is a property of the material. Specific heat is defined as the amount of heat required to raise the temperature of a unit mass of the substance by one degree. For example, for water at 15 °C, C = 1.00kcal / kg − °C = 4.18kJ / kg-°C, which means that it takes 1 kcal of heat to raise the temperature of 1 kg of water from 15 °C to 16 °C.

The definition of specific heat for a gas differs from that of a liquid and solid because the value of specific heat for gases depend upon how the process is carried out. The specific heat values for two particular processes are of special interest to scientists and engineers: constant volume and constant pressure. The values of specific heat at constant volume, cv, and at constant pressure, cp, for gases are quite different. The relationship between these two values of specific heat for an ideal gas is given by

cpcv = Rg

where Rg, the gas constant, and is related to the universal gas constant, Ru, by Rg = Ru / M with M being the molecular mass of the ideal gas. The molecular mass and specific heat for some selected substances are listed in the following table.

Specific heats of different substances at 20 °C

 Substance M (kg/kmol) cp(kJ / kg − oC) cv(kJ / kg − oC) Air 28.97 1.005 0.718 Aluminum 26.9815 0.90 Carbon dioxide 44.01 0.84 0.65 Copper 63.546 0.39 Glass 0.84 Hydrogen 2.016 14.27 10.15 Ice (–5 °C) 18.015 2.10 Iron 55.847 0.45 Lead 207.2 0.13 Marble 0.86 Nitrogen 28.013 1.04 0.74 Oxygen 31.999 0.92 0.66 Steam (100 °C) 18.015 2.02 1.47 Silver 107.868 0.23 Mercury 200.59 0.14 Water 18.015 4.18

Clearly, the values of specific heat for a given gas at constant pressure and constant volume are quite different. For liquids and solids, the specific heat can be assumed to be process-independent, because these phases are nearly incompressible. Therefore, the specific heat of liquids and solids at constant pressure are assumed to apply to all real processes.

## References

Faghri, A., and Zhang, Y., 2006, Transport Phenomena in Multiphase Systems, Elsevier, Burlington, MA.
Faghri, A., Zhang, Y., and Howell, J. R., 2010, Advanced Heat and Mass Transfer, Global Digital Press, Columbia, MO.