EJC Physics H208 Temperature and Ideal Gas 2023 - 1. Notes (full)

Page 1 of 16 9749(202 3) H2 Physics H208 Temperature and Ideal Gases – Notes H2 Topic 8 – Temperature and Ideal Gases Infrared Fever Screening Systems are a common sight in 2020 as the world battles the COVID- 19 pandemic. It was a world-first, made-in-Singapore system back in 2003 to respond to the need for fast, mass measurements of body temperatures when battling the SARS epidemic. The prototype was produced within a week of the Ministry of Health approaching the Defence Science and Technology Agency (DSTA) for assistance. Content • Thermal equilibrium • Temperature scales • Equation of state • Kinetic theory of gases • Kinetic energy of a molecule Learning Outcomes Candidates should be able to: (a) show an understanding that regions of equal temperature are in thermal equilibrium (b) explain how empirical evidence leads to the gas laws and to the idea of an absolute scale of temperature (i.e. the thermodynamic scale that is independent of the property of any particular substance and has an absolute zero) (c) convert temperatures measured in degrees Celsius to kelvin: T / K = T / °C + 273.15 (d) recall and use the equation of state for an ideal gas expressed as pV = nRT, where n is the amount of gas in moles (e) state that one mole of any substance contains 6.02 × 10 23 particles and use the Avogadro number N A = 6.02 × 1023 mol–1 (f) state the basic assumptions of the kinetic theory of gases (g) explain how molecular movement causes the pressure exerted by a gas and hence derive the relationship pV = ⅓ Nm<c2>, where N is the number of gas molecules (a simple model considering one-dimensi onal collisions and then extending to three dimensions using ⅓ <c2> = <cx2> is sufficient) (h) recall and apply the relationship that the mean kinetic energy of a molecule of an ideal gas is proportional to the thermodynamic temperature (i.e. ½ m<c2> = 3 2 kT) to new situations or to solve related problems.

Page 2 of 16 9749(202 3) H2 Physics H208 Temperature and Ideal Gases – Notes 8.0 Introduction Temperature, pressure, and volume are quantities that describe macroscopic properties of a system. Typically, when we discuss them, we refer to a bulk body of gas , liquid or solid. Together, the quantities ( T, p and V) define a state of a system; in the field of thermal physics we refer to gas/liquid/solid as phases. In this field of study of these macroscopic properties, physicists hypothesize simple m icroscopic models to explain the bulk behaviour - that the system consists a large number of objects having complex and random interactions. We often describe the collective behaviour of a large distribution of interacting objects by their statistical averages, which may be more meaningful than the chaos exhibited by individual objects. For example, rather than the individual changes in momentum of gas particles against the inner walls of the container, we describe the statistical average via the bulk property of pressure for a gas. The fact that most real gases generally behave similarly to each other with only slight deviations suggests that the ideal gas model is a good approximation worth studying. Newtonian mechanics and its concepts of kinematics and dynamics is used to model the microscopic motion of gas particles. Microscopic model. Describes the extent of interactions between particles that lead to the bulk (microscopic) behavior – whether it is in the gaseous phase, liquid phase or solid phase.

Page 3 of 16 9749(202 3) H2 Physics H208 Temperature and Ideal Gases – Notes 8.1 Temperature and Thermal Equilibrium To be in thermal contact means the 2 bodies are able to exchange thermal energy. There will be net flow of thermal energy (heat) if the bodies are at different temperatures. Don’t say “ heat energy” as it means “(thermal energy) energy”. also see Annex 1: The Zeroth Law of Thermodynamics Temperature difference between 2 bodies provides 2 pieces of information • direction of thermal energy flow (from higher to lower temperature) • rate (speed) of transfer of thermal energy (the bigger the temperature difference, the faster the rate) When two bodies are in thermal equilibrium, there is no net flow of thermal energy between the bodies that are in thermal contact because they are at equal temperature. Computer chips run hot. There needs to be very good thermal contact between the chip and the heatsink to dissipate the thermal energy built up. Thermal-conducting pastes are placed between the chip and heatsinks to fill in and squeeze out s mall pockets of air because air is an insulator of heat. Heat is thermal energy that flows from a region of higher temperature to a region of lower temperature.

Page 4 of 16 9749(202 3) H2 Physics H208 Temperature and Ideal Gases – Notes 8.2 Measuring Temperature Some thermometric properties used in thermometers: • volume of fixed mass of liquid • resistance of thermistor or resistor • e.m.f. between junctions of dissimilar metals exposed to different temperatures • pressure of fixed mass of gas at constant volume A suitable thermometric property should • vary continuously and uniquely with temperature o different measurements of the thermometric property matches different temperatures in a 1-to-1 mapping • change sufficiently noticeably o a more sensitive thermometer means a larger change in thermometric property for the same temperature change o reduces percentage uncertainty in that temperature measurement • be reproducible 8.2.1 Empirical Centigrade Scales Empirical means “verifiable from observation” . Centigrade means “to divide into 100 steps”. Therefore, an empirical centigrade scale is set up by the following: a) m easure the thermometric property at fixed point of 0 C° (ice point), T0 • pure melting ice in equilibrium with water at standard atmospheric pressure b) m easure the thermometric property at fixed point of 100 C° (steam point), T100 • pure boiling water in equilibrium with steam at standard atmospheric pressure c) a ssume that the thermometric property varies linearly with temperature With this calibration, we measure an unknown temperature Tunknown by measuring its thermometric property Xunknown at the unknown temperature, and using the known values of T0 and T100 in the following equation: unknown 0 unknown 0100 100 CXT X X X ×= − °− Also see Annex 2: Different Types of Thermometer Thermometric property is a property of a substance that changes with temperature. Temperature measurements from empirical centigrade scales across different types of thermometers may not agree because • thermometric properties are assumed to vary linearly with temperature, which is not the case in reality • temperature measurements agree only at fixed points of ice point and steam points T / 0 100 thermometric property X

Page 5 of 16 9749(2022) H2 Physics H208 Temperature and Ideal Gases – Notes thermometer and thermometric property advantages disadvantages liquid-in-glass thermometer measures temperature via changes in volume of a fixed mass of liquid • simple construction • easy to use • portable • fragile • need to surround bulb, so cannot measure temperature at a point/surface • slow response; bulb and glass wall at thermal equilibrium with measured substance mercury-in-glass range of approx. -30 °C to 300 °C higher maximum range than alcohol-in-glass cannot measure temperatures as low as alcohol-in-glass alcohol-in-glass • cheaper than mercury-in-glass • safer when liquid spills during breakage range of approx. −100 °C to 70 °C smaller range than mercury-in-glass resistance thermometer measures temperature via changes in electrical resistance • very accurate when balanced electrically: cannot register