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The molecules are much smaller than the average distance between them, so their total volume is much less than that of their container (which has volume V).To derive the ideal gas law and the connection between microscopic quantities such as the energy of a typical molecule and macroscopic quantities such as temperature, we analyze a sample of an ideal gas in a rigid container, about which we make two further assumptions: The molecules obey Newton’s laws and are in continuous motion, which is random and isotropic, that is, the same in all directions.There is a very large number N of molecules, all identical and each having mass m.First, we make two assumptions about molecules in an ideal gas. We can gain a better understanding of pressure and temperature from the kinetic theory of gases, the theory that relates the macroscopic properties of gases to the motion of the molecules they consist of. Pressure is the force divided by the area on which the force is exerted, and temperature is measured with a thermometer. We have examined pressure and temperature based on their macroscopic definitions.
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Solve problems involving the distance and time between a gas molecule’s collisions.Solve problems involving mixtures of gases.Explain the relations between microscopic and macroscopic quantities in a gas.By the end of this section, you will be able to: