Heat is related to energy in a similar fashion to how work is related to energy. Heat is said to flow from areas of high Temperature to areas of low temperature. Essentially, all objects have a certain amount of energy within them that is related to the random motion of their atoms. This internal energy is directly proportional to the temperature of the object. When two bodies of different temperature come in to thermal contact, they will exchange internal energy until the temperature is equalized. The amount of energy transfered is the amount of heat exchanged. It is a common misconception to confuse heat with internal energy, but there is a difference, and understanding the difference is a necessary part of understanding the [First law of thermodynamics]?.
## Changes of Temperature

## Changes of State

## How Heat Moves

The amount of heat required change the temperature of a material from an initial temperature, T_{0}, to a final temperature, T_{f} depends on the the [heat capacity]? of that material according to the relationship:

Δ H = ∫(T=T_{0}, T=T_{f}) C_{p}(T) dT

The heat capacity is dependent on both the amount of material that is exchanging heat and its properties. The heat capacity can be broken up in several different ways. First of all, it can be represented as a product of mass and specific heat capacity (more commonly called specific heat):

C_{p} = m c_{s}

or the number of moles and the molar heat capacity:

C_{p} = n c_{molar}

Both the molar and specific heat capacities only depend upon the physical properties of the substance being heated, not on any specific properties of the sample. The above definitions of heat capacity only work approximately for solids and liquids, but for gases they don't work at all most of the time. The molar heat capacity can be "patched up" if the changes of temperature occur at either a constant volume or constant pressure. Otherwise, it's generally easiest to use the first law of thermodynamics in combination with an equation relating the internal energy of the gas to its temperature.

A boiling pot of water, at atmospheric pressure, will always be at 100^{o}C no matter how much heat is added. The heat in circumstances such as this is said to be "hidden", and thus it is called **latent heat** (latent is Latin for hidden). Latent heat is the rate of heat per unit mass necessary to change the state of a given substance. Thus:

dQ/dm = L *(should this be a partial derivative or a full one?)*

and:

Q = ∫(m = M_{o}, m = M) L dm

where M_{o} is the amount of mass initially in the new phase, and M is the amount of mass that ends up in the new phase.

L generally doesn't depend on the amount of mass that changes phase, so the equation can normally be written:

Q = L Δm

Sometimes L can be time dependednt if pressure and volume are time varying, so that the integral can be handled:

Q = ∫L (dm/dt) dt

*someone check the above, please, to see if the latent heat really depends on where on the (P, V, T) curve the transition is taking place.*

As mentioned previously, heat tends to move from a high temperature region to a low temperature region. This heat transfer may occur by any of three mechanisms, conduction, convection, and radiation.

Conduction? is the most common means of heat transfer in a solid. On a microscopic scale, conduction occurs as hot, rapidly moving or vibrating atoms and molecules interact with neighboring atoms and molecules, transfering some of their energy (heat) to these neighboring atoms.

Convection? is usually the dominant form of heat transfer in liquids and gases. In convection, heat transfer occurs by the movement of hot or cold portions of the fluid. For example, when water is heated on a stove, hot water from the bottom of the pan rises, heating the water at the top of the pan. Two types of convection are commonly distinguished, *free convection*, in which gravity and buoyancy forces drive the fluid movement, and *forced convection*, where a fan, stirrer, or other means is used to move the fluid.

Radiation is the final means of heat transfer. Radiative heat transfer is the only form of heat transfer that can occur in the absense of any form of material and as such is the only means of heat transfer through a vacuum. Thermal radiation is a direct result of the movements of atoms and molecules in a material. Since these atoms and molecules are composed of charged particles (protons and electrons), their movements result in the emission of electromagnetic radiation, which carries energy away from the surface. At the same time, the surface is constantly bombarded by radiation from the surroundings, resulting in the transfer of energy to the surface. Since the amount of emitted radiation increases with increasing temperature, a net transfer of energy from higher temperatures to lower temperatures results.