The kinetic theory of gases

who steps back and accidentally stomps on your foot with

the heel of one shoe. Would you be better off if that person were (a) a large professional basketball player wearing sneakers (b) a petite woman wearing spike-heeled shoes?

Quick Quiz 4.2 A grandfather clock depends on the period of a pendulum to keep correct time. Suppose a grandfather clock is calibrated correctly and then a mischievous child slides the bob of the pendulum downward on the oscillating rod. Does the grandfather clock run (a) slow (b) fast (c) correctly?

Gases.
Heat Engines, Entropy, and the Second Law of Thermodynamics.

of ideal gas make the following assumptions:

1. The number of

molecules in the gas is large, and the average separation between them is large compared with their dimensions.
2. The molecules obey Newton’s laws of motion, but as a whole they move randomly.
3. The molecules interact only by short-range forces during elastic collisions.
4. The molecules make elastic collisions with the walls.
5. The gas under consideration is a pure substance; that is, all molecules are identical.

is proportional to the number of molecules per unit volume

and to the average translational kinetic energy of the molecules,

a direct measure of average molecular kinetic energy.
(10.3)
(10.4)
(10.5)

freedom contributes ½kbT to the energy of a system, where

possible degrees of freedom in addition to those associated with translation arise from rotation and vibration of molecules.

(10.7)

(10.6)

by heat to a system at constant volume, then no

work is done on the system. From the first law of thermodynamics, we see that

(10.11)

(10.12)

(10.13)

(10.14)

in which no energy is transferred by heat between a

system and its surroundings.

(10.18)

Home work:

important in describing the statistical mechanics of a large number

of molecules. It states that the probability of finding the molecules in a particular energy state varies exponentially as the negative of the energy divided by kBT.

mean free path.

a device that takes in energy by heat and, operating

in a cyclic process, expels a fraction of that energy by means of work.

The net work Weng done by a heat engine is equal to the net energy Qnet transferred to it.

in a cyclic process is the area enclosed by the

curve representing the process on a PV diagram.

(10.23)

The thermal efficiency

(10.24)

engines are well below 100%, the Kelvin–Planck form of the

second law of thermodynamics states the following:

Heat Engines and the Second Law
of Thermodynamics

It is impossible to construct a heat engine that, operating in a cycle, produces no effect other than the input of energy by heat from a reservoir and the performance of an equal amount of work.

construct a cyclical machine whose sole effect is to transfer

energy continuously by heat from one object to another object at a higher temperature without the input of energy by work.

In simpler terms, energy does not transfer spontaneously by heat from a cold object to a hot object.

The effectiveness of a heat pump is described in terms of a number called the coefficient of performance (COP).

(10.25)

(10.26)

the process can be returned to its initial conditions along

the same path on a PV diagram, and every point along this path is an equilibrium state. A process that does not satisfy these requirements is irreversible.

heat engine operating in an ideal, reversible cycle— called a

Carnot cycle—between two energy reservoirs is the most efficient engine possible.

Carnot’s theorem can be stated as follows:

No real heat engine operating between two energy reservoirs can be more efficient than a Carnot engine operating between the same two reservoirs.

between the same two temperatures have the same efficiency.
Hence, the

thermal efficiency of a Carnot engine is

(10.27)

measure of this disorder.
We distinguish between microstates and macrostates of

a system. A microstate is a particular configuration of the individual constituents of the system.
Macrostate is a description of the conditions of the system from a macroscopic point of view and makes use of macroscopic variables such as pressure, density, and temperature for gases.

Because entropy is a measure of disorder, an alternative way of stating this is the entropy of the Universe increases in all real processes.

the end points and therefore is independent of the actual

path followed. Consequently, the entropy change for an irreversible process can be determined by calculating the entropy change for a reversible process that connects the same initial and final states.

(10.28)

(10.29)

a Carnot heat engine that operates between the temperatures Tc

and Th. In one cycle, the engine takes in energy Qh from the hot reservoir and expels energy Qc to the cold reservoir.

(10.30)

very sensitive glass thermometer, which of the following working liquids

would you choose? (a) mercury (b) alcohol (c) gasoline (d) glycerin

metal and have the same radius, but one is hollow

and the other is solid. The spheres are taken through the same temperature increase. Which sphere expands more? (a) solid sphere (b) hollow sphere (c) They expand by the same amount. (d) not enough information to say