Chapter 11 Heat

Heat is a form of energy.

11.1 Mechanical Equivalent of Heat

Heat is a form of energy. Specifically, it is a form of energy that is associated with the random motion of atoms and molecules at a finite temperature.

Calorie: the amount of heat (energy) required to raise the temperature of 1 g of water by 1 degree celsius (kevin).

Joule's experiment: The transfter of mechanical energy into heat.

1 calorie = 4.186 joules

11.2 Specific Heat

The amount of heat (energy) required to raise the temperature of an object by DT is proportional to the mass of the object (not surprisingly). It is also proportional to DT if this this temperature interval does not include the temperature of any phase transitions.

Q = cmDT

The constant c is called the specific heat.

Rewrite this equation as

c = Q/(mDT)

It becomes obvious that Specific heat is the amount of heat (energy) required to raise the temperature of an unit mass of a certain substance by an unit temperature interval. It has a dimension of Energy/(Mass·Temperature), which can be cal/(g·ºC), J/(kg·ºC), or some other variation.

Q < 0 if DT < 0

The physical meaning is that an object releases heat (energy) as its temperature drops. We are using the convention that the amount of heat absorbed by the object is positive, the amount of heat released is correspondingly negative.

11.3 Conservation of Energy: Calorimetry

Heat is a form of energy and energy is conserved.

Energy conservation:

DE = 0
Ef = Ei

for an isolated system.

Mixture type of problem

From the conservation of energy, we can measure the specific heat of one substance by mixing it with another substance of known specific heat.

Specifically, we need to measure the masses and the initial temperatures of both substances, and the final temperature after the mixing.


DE = DEx + DEw = cxmx(T-Txi) + cwmw(T-Twi) = 0

(the LHS as the total change of energy), or

-DEx = cxmx(Txi-T) = DEw = cwmw(T-Twi)

we obtain

cx = cwmw(T-Twi)/[mx(Txi-T)]

If you do not know the specific heat of the other substance, this procedure still allows you to determine the ratio of the two specific heat.

cx/cw = mw(T-Twi)/[mx(Txi-T)]

Example 11.2. is a specific example.

11.4 Latent heat and Phase Changes

A substance can be different phases which differ from each other in their internal arrangements of contituent atoms and molecules. A transition from one phase to another is called a phase transition.

Under a fixed pressure, a phase transition occurs at a specific temperature which is called the transition temperature. Temperature does not change during a phase transition, what changes is the internal arrangement of atoms and molecules.

Figure 11.3

Latent heat: the amount of heat (energy) required to change the phase of an unit mass of a substance.

This definition makes sense because the amount of heat (energy) required to change the phase of an object should obviously be proportional to the mass of the object:

Q = mL

The constant of proportionality is what we defined as the latent heat and is given by

L = Q/m

It has a dimension of Energy/Mass, which can be cal/g, J/kg, or some other variation.

Heat (energy) is required to melt a substance (solid to liquid phase transition). The corresponding latent heat is called the latent heat of fusion. When a substance solidifies, it releases heat.

Heat (energy) is required to vaporize a substance (liquid to gas phase transition). The corresponding latent heat is called the latent heat of vaporization. A substance releases heat when it condenses into liquid.

Example 11.4

We need an amount of steam which, during its process of becoming water at 50 ºC, releases sufficient heat (energy) to raise the temperature of both the water and the glass to 50 ºC.


11.5 Heat Transfer by Conduction

Heat (thermal energy) flows spontaneously from regions of high temperature to regions of low temperature. This transfer of heat can happen through different mechanisms: conduction, convection, and radiation.

In Heat conduction, thermal energy is transferred through the interactions between atoms, molecules, and electrons. The heated substance itself does not move, but the energy is passed on through interactions.

The conductive heat transfer is described by the equation:

H = Q/Dt = kA[(T2-T1)/L]


Putting it in words:

The amount of heat transfer through a cross section per unit time is proportional to the area of the cross section (quite obviously) and the temperature gradient (T2-T1)/L. The constant of proportion is called the thermal conductivity.

Note that what matters here is how fast the temperature changes. A thicker wall is better than a thinner wall, as far as heat insulation is concerned.

Dense substances such as metal are usually good heat conductors. Dilute substances such as air are poor heat conductors.

A good heat conductor feels colder (or hotter) than a poor heat conductor at the same temperature because it transfers heat more quickly.

11.6 Convection

Convection refers to heat transfer through the movement of heated substance.

Natural Convection: The heated substance expands, becomes less dense and rises.

Forced Convection: The motion is forced (by a fan for example).

11.7 Radiation

Heat can be transported by radiation because radiation carries energy.

An object at any finite temperature is constantly emitting and absorbing radiation. The rate at which an object emits radiant energy is proportional to the fourth power of its absolute temperature. This is known as the Stefan's law

P = sAeT4


If we put the object in surrounding which is at temperature T0, the net power of energy exchange is given by

Pnet = sAe(T4-T04)

because the object also absorbs energy from its environment.

Radiation is the only way an object can gain or loose heat (energy) if it is surrounded by a vaccum (assuming it is not emitting other particles).

An object eventually reaches thermal equilibrium (through heat transfer mechanisms we are looking at) with its environment if it does not have any source (or sink) of energy. Warm house in the winter and cool house in the summer both require energy to maintain (you would have a stronger impression of this if you are paying the electric or gas bills)

Cooling of a cup of coffee:

A complex combination of these mechanisms +
Cooling by evaporation (which is what makes the observation of Bose-Einstein condenstion in a dilute atomic vapor possible).

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Copyright © 1997 by Bo Gao. All rights reserved.