Temperature and Ideal Gases JPJC Notes

1 JURONG PIONEER JUNIOR COLLEGE 9749 H2 PHYSICS 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 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 236.02 10 particles and use the Avogadro number 236.02 10AN = 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 21 3pV Nm c= , where N is the number of gas molecules (a simple model considering one -dimensional collisions and then extending to three dimensions using 22 1 3 xcc = 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. 213 22m c kT= ) to new situations or to solve related problems.

2 Introduction 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. Linking these two ideas is the concept of thermal equilibrium. The properties of matter depend on temperature, pressure, volume, etc. The condition in which a particular material exists is known as its state, and this could be described by such macroscopic physical quantities, including its mass, which is a measure of the amount of substance. Most gases at room temperature and atmospheric pressure behave approximately like ideal gases. The ideal gas equation expresses the relationship between state variables for an ideal gas. The kinetic theory of gases is a simple e xample of a link between macroscopic properties (pressure, volume, temperature) with microscopic properties (mass and speed of randomly - moving individual molecules that make up a gas). To a good approximation, we can use Newtonian mechanics to model the mi croscopic motion of gas molecules, and we can apply concepts from kinematics and dynamics to analyse the average pressure exerted by the randomly-moving molecules. 1 Thermal equilibrium 1.1 Temperature ▪ Temperature is a property of a body or system.