# From Heat TO Time-Invariance

FROM HEAT TO TIME-INVARIANCE

Spilled milk never returns into its container by itself. Any hot object, left alone, cools

down with time; it never heats up.These and many other observations show that numerous

processes in nature are irreversible. Does this mean that motion is not time-reversalinvariant,

as Nobel Prize winner Ilya Prigogine thought? We discuss the issue in this

section.

All irreversible phenomena involve heat.Thus we need to know the basic facts about

heat in order Ref. 250 to discuss irreversibility.The main points that are taught in high school are

almost sufficient.

Temperature

Macroscopic bodies, i.e., bodies made of many atoms, have temperature. The temperature

of a macroscopic body is an aspect of its state. It is observed that any two bodies in

contact tend towards the same temperature: temperature is contagious. In other words,

temperature describes an equilibriumsituation.The existence and contagiousness of temperature

is often called the zeroth principle of thermodynamics. Heating is the increase of

temperature, cooling its decrease.

How is temperaturemeasured?The eighteenth century produced the clearest answer:

temperature is best defined and measured by the expansion of gases. For the simplest, socalled

ideal gases, the product of pressure p and volumeV is proportional to temperature:

pV ∼ T. (104)

The proportionality constant is fixed by the amount of gas used. (More about it shortly.)

The ideal gas relation allows us to determine temperature by measuring pressure and

volume.This is the way (absolute) temperature has been defined and measured for about

Ref. 251 a century. To define the unit of temperature, one only has to fix the amount of gas used. It

Page 347 is customary to fix the amount of gas at 1mol; for oxygen this is 32 g.The proportionality

constant, called the ideal gas constant R, is defined tobe R = 8.3145 J/mol K.This number

has been chosen in order to yield the best approximation to the independently defined

Celsius temperature scale. Fixing the ideal gas constant in this way defines 1K, or one

Kelvin, as the unit of temperature. In simple terms, a temperature increase of one Kelvin

is defined as the temperature increase that makes the volume of an ideal gas increase –

Challenge 548 ny keeping the pressure fixed – by a fraction of 1/273.15 or 0.3661%.

Temperature is an aspect of the state of a body. In other words, two identical bodies

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