ASRJC Temperature and Ideal Gases Notes

ANDERSON SERANGOON JUNIOR COLLEGE PHYSICS 9749 8-1 Additional Notes Topic 8: Temperature and Ideal Gases 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 Kelvin to degrees Celsius: 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 x 1023 particles and use the Avogadro number NA = 6.02 x 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 = 1/3 Nm<c2>, where N is the number of gas molecules ( a simple model considering one -dimensional collisions and then extending to three dimensions using 1/3 <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 Nature of Science Heat and temperature are often used interchangeably in everyday language. However, these terms have different and specific meanings in physics. Macroscopically, temperature can be defined in terms of its measurement, while heat refers to the energy transferred between two systems at different temperatures. Understanding thermal physics requires us to approach the concepts from both the macroscopic and microscopic lenses.

ANDERSON SERANGOON JUNIOR COLLEGE PHYSICS 9749 8-2 Additional Notes A.1 Temperature, Heat and Internal Energy • The temperature of a system is a measure of its average molecular kinetic energy. A higher temperature implies that the molecules in the system are moving faster on average. • Heating (thermal energy supplied) is a transfer of energy to an object resulting in an increase in the random kinetic and/or potential energies of the atoms or molecules of the object. • Internal energy is the sum of a random distribution of kinetic and potential energies associated with the molecules of a system. • When a body absorbs heat, two situations may arise: 1. The particles move further apart (increased molecular PE), causing an expansion. They also move more quickly on the average (increased molecular KE), causing a rise in temperature. 2. The particles move further apart (increased molecular PE), causing an expansion. However, they move with the same speed on average (same molecular KE), hence there is no change in temperature. o In other words, i t is p ossible to supply heat to a body without causing a change in its temperature. This happens when the heat added to a body increases its molecular potential energy (PE) while leaving molecular kinetic energy (KE) unchanged. E.g. when water is boiling, when ice is melting. o Similarly, it is possible to remove heat from a body without causing a change in its temperature. This happens when the heat removed from a body decreases its molecular potential energy (PE) while leaving molecular kinetic energy (KE) unchanged. E.g. when water is freezing. Check Your Understanding 1. Temperature of a system is a measure of its average molecular kinetic energy and molecular potential energy. (True / False) 2. It is possible for a body to absorb heat without causing a change in its temperature. (True / False) Relating Science and Society Many researchers still actively investigate the behaviour of gases using computer simulation and other techniques. Environmental problems connected with Earth’s atmosphere, such as the depletion of the ozone layer and the unwanted discharge of thermal energy into the environment known as thermal pollution, are motivations for such work. A better understanding of the behaviour of gases might lead to an improved characterisation and possible solutions to these problems. A Temperature Scales Note: Thermal energy is not internal energy. Refer to Topic 9 “First Law of Thermodyn amics” for more information about thermal energy and internal energy.

ANDERSON SERANGOON JUNIOR COLLEGE PHYSICS 9749 8-3 Additional Notes A.2 Thermal Equilibrium • When objects or substances are in contact such that heat is able to flow from one object or substance to another, they are said to be in thermal contact. • When two bodies in thermal contact have the same temperature and there is no net flow of heat between them, the two bodies are said to be in thermal equilibrium. • When two bodies are in thermal equilibrium, their temperatures are the same. • Therefore, the temperature of a body is the physical property which determines whether the body will be in thermal equilibrium with another body. A.3 Temperature Scales • A thermometer is calibrated according to a temperature scale. • Two temperature scales, the empirical scale and the thermodynamic scale have been established. • They are established by making use of reference or fixed points. The Empirical Scale • The empirical scale of temperature is a scale of temperature that is based on the variation with temperature of a property of a substance, assuming that the property varies linearly with temperature although it may not necessarily be so. • An example is the Centigrade scale used in a mercury thermometer. This empirical scale of temperature is based on the expansion of mercury’s volume with rising temperature. • At melting point of ice (0 ºC) and the steam point (100 ºC) which are fixed points, the respective values of thermometric property X are measured as Xo and X100. • To calculate an unknown temperature , the corresponding thermometric property X is measured.  can be calculated as Zeroth Law of Thermodynamics If two bodies X and Y are separately in thermal equilibrium with a third body T, then X and Y are in thermal equilibrium with each other. Memorise 100− −= o100 o XX XX  0 Xo  100 X100 X Property, X Temperature/ oC

ANDERSON SERANGOON JUNIOR COLLEGE PHYSICS 9749 8-4 Additional Notes Worked Example A resistance thermometer has a resistance of 9.97 Ω at the ice point and 14.04 Ω at the steam point. Find the temperature on the centigrade scale of this thermometer when its resistance is 11.51 Ω. Thermodynamic Scale of Temperature • Empirical scale may agree at the calibration points of, for example 0 ⁰C and 100 ⁰C but not at intermediate temperatures. • Hence, we want an ideal temperature scale that does not depend on the properties of a particular material. • The gas thermometer comes closest to this ideal temperature scale. • The principle of a gas thermometer is that the pressure of a gas at constant volume increases with temperature. A quantity of gas is placed in a constant volume container and its pressure is measured at 0 C and 100 C, say; and a straight line drawn. • Graphs of pressure versus temperature at constant volume for three different types and quantities of gas are plotted. • Extrapolation of the graph shows a hypothetical temperature –273.15 ⁰C at which absolute pressure of gas would become zero for different quantities of gas used as well as different gases used. • We use this extrapolated zero