#set document(title: "1.1 Temperature and Thermal Equilibrium", author: "OpenStax / XYZ Homework") #set page(width: 8.5in, height: auto, margin: 1in) #import "@preview/cetz:0.5.2" #set text(font: ("STIX Two Text", "Libertinus Serif", "New Computer Modern"), size: 10.5pt, lang: "en") #show math.equation: set text(font: ("STIX Two Math", "New Computer Modern Math")) #set par(justify: true, leading: 0.62em, spacing: 0.9em) #set enum(spacing: 1.1em) // room between list items so tall inline fractions don't collide #set list(spacing: 1.1em) #set table(stroke: 0.5pt + rgb("#c7ccd3")) #let BLUE = rgb("#183B6F") // brand navy — section bars + example/solution labels (white on navy 11.09:1) #let ORANGE = rgb("#A94509") // brand primary-700 — AA-safe deep orange for TEXT (5.93:1 on white; raw brand #F37021 is 2.94:1 and must never carry text) #let RED = rgb("#DC2626") // brand error-600 #let GREEN = rgb("#059669") // brand success-600 (decoration only; small green text uses green-text #007942) #show heading.where(level: 1): it => block(width: 100%, above: 0pt, below: 16pt, fill: gradient.linear(BLUE, rgb("#2C5AA0")), inset: (x: 14pt, y: 12pt), radius: 3pt, text(fill: white, weight: "bold", size: 19pt, it.body)) #show heading.where(level: 2): it => block(width: 100%, above: 18pt, below: 10pt, fill: BLUE, inset: (x: 10pt, y: 6pt), radius: 2pt, text(fill: white, weight: "bold", size: 12pt, it.body)) #show heading.where(level: 3): it => text(fill: ORANGE, weight: "bold", size: 12.5pt, it.body) #show heading.where(level: 4): it => text(fill: BLUE, weight: "bold", size: 10.5pt, it.body) #let examplebox(label, title, body) = block(width: 100%, breakable: true, fill: rgb("#EFF1F5"), stroke: 0.5pt + rgb("#CFDDF0"), radius: 4pt, inset: 10pt, above: 12pt, below: 12pt)[ #block(below: 6pt)[#box(fill: BLUE, inset: (x: 6pt, y: 2pt), radius: 2pt, text(fill: white, weight: "bold", size: 8.5pt, label)) #h(0.4em) #strong[#title]] #body] // rail = decorative left rule (raw brand token); labelcolor = AA-safe label text shade #let notebox(label, rail, labelcolor, tint, body) = block(width: 100%, breakable: true, fill: tint, stroke: (left: 3pt + rail), inset: (left: 10pt, rest: 8pt), radius: (right: 4pt), above: 11pt, below: 11pt)[ #text(fill: labelcolor, weight: "bold", size: 7.5pt, tracking: 0.5pt)[#upper(label)] #linebreak() #body] #let solutionbox(body) = block(above: 4pt, below: 8pt)[ #text(fill: BLUE, weight: "bold", size: 8.5pt)[Solution] #linebreak() #body] #let figph(msg) = block(width: 100%, height: 60pt, fill: rgb("#f6f7f9"), stroke: (paint: rgb("#c7ccd3"), dash: "dashed"), radius: 4pt, inset: 10pt)[ #align(center + horizon, text(fill: rgb("#889"), style: "italic", size: 9pt, msg))] // Standardize inlined figure sizes: measure the natural CeTZ canvas, then scale to a // consistent envelope (aspect-aware; see build_typst.py FIG_* constants). Unlike the // print preamble, dimensions are FLOORED: in an editor a user can trim a figure to a // degenerate 1-D shape (a bare line), and w/h or tw/w would then divide by zero. #let _STD_W = 3.5 #let _WIDE_W = 5.6 #let _MAX_H = 3.4 #let _ASPECT_WIDE = 2.2 #let _UPSCALE_MAX = 1.15 #let stdfig(body) = context { let m = measure(body) let w = calc.max(m.width / 1in, 0.01) let h = calc.max(m.height / 1in, 0.01) let tw = if w / h > _ASPECT_WIDE { _WIDE_W } else { _STD_W } let s = calc.min(tw / w, _MAX_H / h, _UPSCALE_MAX) align(center, box(scale(x: s * 100%, y: s * 100%, reflow: true, body))) } #show figure: set block(breakable: false) #set figure(gap: 8pt) #show figure.caption: set text(size: 8.5pt, fill: rgb("#555")) == 1.1#h(0.6em)Temperature and Thermal Equilibrium Heat is familiar to all of us. We can feel heat entering our bodies from the summer Sun or from hot coffee or tea after a winter stroll. We can also feel heat leaving our bodies as we feel the chill of night or the cooling effect of sweat after exercise. What is heat? How do we define it and how is it related to temperature? What are the effects of heat and how does it flow from place to place? We will find that, in spite of the richness of the phenomena, a small set of underlying physical principles unites these subjects and ties them to other fields. We start by examining temperature and how to define and measure it. === Temperature The concept of temperature has evolved from the common concepts of hot and cold. The scientific definition of temperature explains more than our senses of hot and cold. As you may have already learned, many physical quantities are defined solely in terms of how they are observed or measured, that is, they are defined #emph[operationally]. #strong[Temperature] is operationally defined as the quantity of what we measure with a thermometer. As we will see in detail in a later chapter on the kinetic theory of gases, #strong[temperature] is proportional to the average kinetic energy of translation, a fact that provides a more physical definition. Differences in temperature maintain the transfer of heat, or #emph[heat transfe]r, throughout the universe. #strong[Heat transfer] is the movement of energy from one place or material to another as a result of a difference in temperature. (You will learn more about #strong[heat transfer] later in this chapter.) === Thermal Equilibrium An important concept related to temperature is #strong[thermal equilibrium]. Two objects are in thermal equilibrium if they are in close contact that allows either to gain energy from the other, but nevertheless, no net energy is transferred between them, or, even when not in contact, if no net energy is transferred between them when they are brought into contact. If two objects remain in contact for a long time, they typically come to equilibrium. In other words, two objects in thermal equilibrium do not exchange energy. Experimentally, if object #emph[A] is in equilibrium with object #emph[B], and object #emph[B] is in equilibrium with object #emph[C], then (as you may have already guessed) object #emph[A] is in equilibrium with object #emph[C]. That statement of transitivity is called the #strong[zeroth law of thermodynamics]. (The number “zeroth” was suggested by British physicist Ralph Fowler in the 1930s. The first, second, and third laws of thermodynamics were already named and numbered then. The zeroth law had seldom been stated, but it needs to be discussed before the others, so Fowler gave it a smaller number.) Consider the case where #emph[A] is a thermometer. The zeroth law tells us that if #emph[A] reads a certain temperature when in equilibrium with #emph[B], and it is then placed in contact with #emph[C], it will not exchange energy with #emph[C]; therefore, its temperature reading will remain the same . In other words, #emph[if two objects are in thermal equilibrium, they have the same temperature]. #figure(figph[The figure on the left shows two boxes labeled B and C in contact with each other. A thermometer A is attached to box B. The figure on the right shows the same boxes, with the thermometer attached to box C. In both cases, the temperature reading on the thermometer is the same.], alt: "The figure on the left shows two boxes labeled B and C in contact with each other. A thermometer A is attached to box B. The figure on the right shows the same boxes, with the thermometer attached to box C. In both cases, the temperature reading on the thermometer is the same.", caption: [If thermometer #emph[A] is in thermal equilibrium with object #emph[B], and #emph[B] is in thermal equilibrium with #emph[C], then #emph[A] is in thermal equilibrium with #emph[C]. Therefore, the reading on #emph[A] stays the same when #emph[A] is moved over to make contact with #emph[C].]) A thermometer measures its own temperature. It is through the concepts of thermal equilibrium and the zeroth law of thermodynamics that we can say that a thermometer measures the temperature of #emph[something else,] and to make sense of the statement that two objects are at the same temperature. In the rest of this chapter, we will often refer to “systems” instead of “objects.” As in the chapter on linear momentum and collisions, a system consists of one or more objects—but in thermodynamics, we require a system to be macroscopic, that is, to consist of a huge number (such as #math.equation(block: false, alt: "10 to the power 23")[$10^(23)$]) of molecules. Then we can say that a system is in thermal equilibrium with itself if all parts of it are at the same temperature. (We will return to the definition of a thermodynamic system in the chapter on the first law of thermodynamics.) === Summary - Temperature is operationally defined as the quantity measured by a thermometer. It is proportional to the average kinetic energy of atoms and molecules in a system. - Thermal equilibrium occurs when two bodies can freely exchange energy but no net energy is transferred between them. - The zeroth law of thermodynamics states that when two systems, #emph[A] and #emph[B,] are in thermal equilibrium with each other, and #emph[B] is in thermal equilibrium with a third system #emph[C], then #emph[A] is also in thermal equilibrium with #emph[C]. === Conceptual Questions What does it mean to say that two systems are in thermal equilibrium? #solutionbox[ They are at the same temperature, and if they are placed in contact, no net heat flows between them. ] Give an example in which #emph[A] has some kind of non-thermal equilibrium relationship with #emph[B], and #emph[B] has the same relationship with #emph[C], but #emph[A] does not have that relationship with #emph[C].