Heat in Thermodynamics

zeroth-law-of-thermodynamics-heatWhile internal energy refers to the total energy of all the molecules within the object, heat is the amount of energy flowing from one body to another spontaneously due to their temperature difference. Heat is a form of energy, but it is energy in transit. Heat is not a property of a system. However, the transfer of energy as heat occurs at the molecular level as a result of a temperature difference.

Consider a block of metal at high temperature, that consists of atoms that are oscillating intensely around their average positions. At low temperatures, the atoms continue to oscillate, but with less intensity. If a hotter block of metal is put in contact with a cooler block, the intensely oscillating atoms at the edge of the hotter block gives off its kinetic energy to the less oscillating atoms at the edge of the cool block. In this case there is energy transfer between these two blocks and heat flows from the hotter to the cooler block by this random vibrations.

In general, when two objects are brought into thermal contact, heat will flow between them until they come into equilibrium with each other.  When a temperature difference does exist heat flows spontaneously from the warmer system to the colder system. Heat transfer occurs by conduction or by thermal radiation. When the flow of heat stops, they are said to be at the same temperature. They are then said to be in thermal equilibrium.

As with work, the amount of heat transferred depends upon the path and not simply on the initial and final conditions of the system. There are actually many ways to take the gas from state i to state f.

Also, as with work, it is important to distinguish between heat added to a system from its surroundings and heat removed from a system to its surroundings. Q is positive for heat added to the system, so if heat leaves the system, Q is negative. Because W in the equation is the work done by the system, then if work is done on the system, W will be negative and Eint will increase.

The symbol q is sometimes used to indicate the heat added to or removed from a system per unit mass. It equals the total heat (Q) added or removed divided by the mass (m).

Heat Capacity

Table of specific heat capacitiesDifferent substances are affected to different magnitudes by the addition of heat. When a given amount of heat is added to different substances, their temperatures increase by different amounts. This proportionality constant between the heat Q that the object absorbs or loses and the resulting temperature change T of the object is known as the heat capacity C of an object.

C = Q / ΔT

Heat capacity is an extensive property of matter, meaning it is proportional to the size of the system. Heat capacity C has the unit of energy per degree or energy per kelvin. When expressing the same phenomenon as an intensive property, the heat capacity is divided by the amount of substance, mass, or volume, thus the quantity is independent of the size or extent of the sample.

Specific Heat Capacity

The heat capacity of a substance per unit mass is called the specific heat capacity (cp) of the substance. The subscript p indicates that the heat capacity and specific heat capacity apply when the heat is added or removed at constant pressure.

cp = Q / mΔT

Specific Heat Capacity

In the Ideal Gas Model, the intensive properties cv and cp are defined for pure, simple compressible substances as partial derivatives of the internal energy u(T, v) and enthalpy h(T, p), respectively:

Specific Heat at Constant Volume and Constant Pressure

where the subscripts v and p denote the variables held fixed during differentiation. The properties cv and cp are referred to as specific heats (or heat capacities) because under certain special conditions they relate the temperature change of a system to the amount of energy added by heat transfer. Their SI units are J/kg K or J/mol K. Two specific heats are defined for gases, one for constant volume (cv) and one for constant pressure (cp).

Molar specific heats - ideal gasAccording to the first law of thermodynamics, for constant volume process with a monatomic ideal gas the molar specific heat will be:

Cv = 3/2R = 12.5 J/mol K


U = 3/2nRT

It can be derived that the molar specific heat at constant pressure is:

Cp = Cv + R = 5/2R = 20.8 J/mol K

This Cp is greater than the molar specific heat at constant volume Cv, because energy must now be supplied not only to raise the temperature of the gas but also for the gas to do work because in this case volume changes.

Latent Heat of Vaporization

Latent heat of vaporization - water at 0.1 MPa, 3 MPa, 16 MPa

The heat of vaporization diminishes with increasing pressure, while the boiling point increases. It vanishes completely at a certain point called the critical point.

In general, when a material changes phase from solid to liquid, or from liquid to gas a certain amount of energy is involved in this change of phase. In case of liquid to gas phase change, this amount of energy is known as the enthalpy of vaporization, (symbol ∆Hvap; unit: J) also known as the (latent) heat of vaporization or heat of evaporation. Latent heat is the amount of heat added to or removed from a substance to produce a change in phase. This energy breaks down the intermolecular attractive forces, and also must provide the energy necessary to expand the gas (the pΔV work). When latent heat is added, no temperature change occurs. The enthalpy of vaporization is a function of the pressure at which that transformation takes place.

Latent heat of vaporization – water at 0.1 MPa (atmospheric pressure)

hlg = 2257 kJ/kg

Latent heat of vaporization – water at 3 MPa (pressure inside a steam generator)

hlg = 1795 kJ/kg

Latent heat of vaporization – water at 16 MPa (pressure inside a pressurizer)

hlg = 931 kJ/kg

The heat of vaporization diminishes with increasing pressure, while the boiling point increases. It vanishes completely at a certain point called the critical point. Above the critical point, the liquid and vapor phases are indistinguishable, and the substance is called a supercritical fluid.

The heat of vaporization is the heat required to completely vaporize a unit of saturated liquid (or condense a unit mass of saturated vapor) and it equal to hlg = hg − hl.

The heat that is necessary to melt (or freeze) a unit mass at the substance at constant pressure is the heat of fusion and is equal to hsl = hl − hs, where hs is the enthalpy of saturated solid and hl is the enthalpy of saturated liquid.

Phase changes - enthalpy of vaporization

Latent heat of vaporization – water at 0.1 MPa. Dominant part of heat absorbed.

Nuclear and Reactor Physics:

  1. J. R. Lamarsh, Introduction to Nuclear Reactor Theory, 2nd ed., Addison-Wesley, Reading, MA (1983).
  2. J. R. Lamarsh, A. J. Baratta, Introduction to Nuclear Engineering, 3d ed., Prentice-Hall, 2001, ISBN: 0-201-82498-1.
  3. W. M. Stacey, Nuclear Reactor Physics, John Wiley & Sons, 2001, ISBN: 0- 471-39127-1.
  4. Glasstone, Sesonske. Nuclear Reactor Engineering: Reactor Systems Engineering, Springer; 4th edition, 1994, ISBN: 978-0412985317
  5. W.S.C. Williams. Nuclear and Particle Physics. Clarendon Press; 1 edition, 1991, ISBN: 978-0198520467
  6. Kenneth S. Krane. Introductory Nuclear Physics, 3rd Edition, Wiley, 1987, ISBN 978-0471805533
  7. G.R.Keepin. Physics of Nuclear Kinetics. Addison-Wesley Pub. Co; 1st edition, 1965
  8. Robert Reed Burn, Introduction to Nuclear Reactor Operation, 1988.
  9. U.S. Department of Energy, Nuclear Physics and Reactor Theory. DOE Fundamentals Handbook, Volume 1 and 2. January 1993.

Advanced Reactor Physics:

  1. K. O. Ott, W. A. Bezella, Introductory Nuclear Reactor Statics, American Nuclear Society, Revised edition (1989), 1989, ISBN: 0-894-48033-2.
  2. K. O. Ott, R. J. Neuhold, Introductory Nuclear Reactor Dynamics, American Nuclear Society, 1985, ISBN: 0-894-48029-4.
  3. D. L. Hetrick, Dynamics of Nuclear Reactors, American Nuclear Society, 1993, ISBN: 0-894-48453-2. 
  4. E. E. Lewis, W. F. Miller, Computational Methods of Neutron Transport, American Nuclear Society, 1993, ISBN: 0-894-48452-4.

See above: