RI Chap 12 Temperature and Ideal Gases Notes

12 TEMPERATURE & IDEAL GASES H2 Physics 9478 Content Page 12.1 Temperature scales 3 12.2 Equation of state 7 12.3 Kinetic theory of gases 11 12.4 Appendix 15 Learning Outcomes Candidates should be able to: (a) show an understanding that a thermodynamic scale of temperature has an absolute zero and is independent of the property of any particular substance. (b) convert temperatures measured in degrees Celsius to kelvin: / K / °C 273.15T θ= + . (c) recall and use the equation of state for an ideal gas expressed as pV NkT= , where N is the number of particles. (d) state that one mole of any substance contains 236.02 10× particles, and use the Avogadro constant 23 16.02 10 molAN −= × as well as the relationship Nk nR= between the Boltzmann constant and the molar gas constant (n is the amount of substance in moles). (e) state the basic assumptions of the kinetic theory of gases. (f) explain how the random motion of gas particles exert mechanical pressure and hence derive, using the definition of pressure as force per unit area, the relationship 21 3pV Nm c= (a simple model considering one -dimensional collisions and then extending to three dimensions using 22 1 3 xcc = is sufficient). (g) recall and use the relationship that the mean translational kinetic energy of a particle of an ideal gas is (directly) proportional to the thermodynamic temperature ( i.e., 213 22m c kT= ) to solve problems.

Page | 2 Temperature and Ideal Gases – An Overview Concepts such as speed, velocity, force and kinetic energy are carefully defined to make the study of mechanics quantitative. Similarly, there needs to be careful definition of terms like temperature, heat and internal energy, which are used in thermal physics. Understanding thermal physics requires us to approach the concepts from both the macroscopic and microscopic perspectives. Heat and temperature are often used interchangeably by the lay-person. However, these terms have different and specific meanings in physics. Macroscopically, temperature can be defined in terms of its measurement using a thermometer, while heat refers to the energy transferred between two systems due to a temperature difference between them. A thermometer is used to measure temperature and it is calibrated according to a temperature scale. The Kelvin scale has a privileged status, as it is independent of the physical properties of the medium used for temperature measurement. This is unlike the Celsius scale, commonly used in liquid-in-glass thermometers, which is calibrated based on the properties of water. Generally, the physical properties of a substance depend on physical quantities such as temperature, pressure and volume. The condition in which a particular material exists is known as its state, and this could be described by such macroscopic physical quantities. We are particularly interested in the study of gases as their volumes can be varied much more d