Lecture 37 Temperature and 0th law of thermodynamics Thermal equilibrium Temperature Temperature scale Thermometer Ideal gas and equation of ideal gas Pressure and temperature from the microscopic point of view

Fundamental problems about thermodynamics Thermodynamics is a branch of physics concerned with heat and temperature and their relation to energy and work. What is temperature and how to define it? What is heat? What is its relation to work How efficient can heat to transformed into work What may happen on matters when temperature changes?

Intensive and extensive properties of a bulk system An intensive property（内涵）is a bulk property, meaning that it is a physical property of a system that does not depend on the system size or the amount of material in the system. density, pressure, …. An extensive property (外延）is one that is additive for independent, noninteracting subsystems. The property is proportional to the amount of material in the system. Mass, volume…

Equilibrium state A system is said to be in thermal equilibrium when it experiences no net change of its observable state over time. The intensive parameters in a equilibrium system are homogeneous throughout the whole system Can we use pressure, temperature and volume to describe the air of a room with a working electric fan?

Zeroth law of thermodynamics The zeroth law of thermodynamics states that if two thermodynamic systems are each in thermal equilibrium with a third, then all three are in thermal equilibrium with each other. If a body A, be in thermal equilibrium with two other bodies, B and C, then B and C are in thermal equilibrium with one another.

Thermometers The most precise statement of the zeroth law is that thermal equilibrium constitutes an equivalence relation on pairs of thermodynamic systems. The zeroth law justifies the use of suitable thermodynamic systems as thermometers to provide such a labeling, which yield any number of possible empirical temperature scales. Such temperature scales bring additional continuity and ordering (i.e., "hot" and "cold") properties to the concept of temperature.

Temperature A temperature is a comparative objective measure of hot and cold. How to define and measure temperature? Physical system changes when temperature changes. Thermal expansion and contraction in volume Define temperature by making use of the change of some properties of physical system

Celsius scale Define the temperature of the freezing point of water as 0℃, and the temperature of its boiling point temperature as 100℃. How to define 1℃? Define the temperature being linear change with its length or volume or something else.

Are these two thermometers the same? 1742  Swedish astronomer Anders Celsius

Defining and measuring temp has always being a challenge The surface temperature of the sun? The inner temperature of the sun? The inner temperature of the earth How cold can things get? How to get ever cold system? Temperature of a cold atomic system? (Nobel prize for W. Phillips)

Ideal gas What distinguishes a gas from liquids and solids is the vast separation of the individual gas particles. An ideal gas is a theoretical gas composed of many randomly moving point particles that do not interact except when they collide elastically.

Equation of state For a gas, one can describe its state by temperature, volume, and pressure For real gases at low density and high temperature, one can find 𝑝𝑉=𝑛𝑅𝑇 where n is the amount of gas, 𝑅 is gas constant 𝑅=8.3144621 75 𝐽 𝑚𝑜𝑙 𝐾 The equation is called ideal gas law.

Constant pressure thermometer Calibrate temperature by making using volume of gas with constant pressure

Constant volume thermometer Calibrate temperature by making using pressure of gas with constant volume

Meaning of temperature Are these two the same? Yes, in ideal gas! But in a real system, this might be different. So what is the precise meaning of temp? We can only know through a microscopic description.

The coldest we can ever get? Early experiments observed changes in pressure or volume as temperature changed. It was noticed that the linear trends lead to a consistent lowest temperature that we call “absolute zero”—labeled 0K after Lord Kelvin.

Ideal gas scale and Kelvin 𝑇= 𝑇 𝑐 +273.15 where 𝑇 𝑐 is Celsius temperature The Kelvin is a unit of measure for temperature. A Kelvin is defined as the fraction 1⁄273.16 of the thermodynamic temperature of the triple point of water (exactly 0.01℃)

Magneto-optical trap A magneto-optical trap (abbreviated MOT) is an apparatus that uses laser cooling with magneto- optical trapping in order to produce samples of cold, trapped, neutral atoms at temperatures as low as several microkelvins Steven Chu