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Chapter 16. Temperature and the Kinetic Theory of Gases. Temperature scales. Absolute zero. State of a System. System: an object under consideration, an example we will use often is a box of gas.

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## Temperature and the Kinetic Theory of Gases

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**Chapter 16**Temperature and the Kinetic Theory of Gases**State of a System**System: an object under consideration, an example we will use often is a box of gas. State variables: variables that give us information about the macroscopic state (or property) of a system. P, V, T, m, n, … Equation of state: an equation that relates the state variables. PV=nRT**The Ideal Gas Law**Ideal gas: A gas of point particles which has no other interactions besides collision among molecules. No intermolecular force.**Atm, STP and other loose ends**A common non-SI unit for pressure is atm (atmospheric pressure), but make sure it is converted to Pa before you apply the ideal gas law. STP or Standard Temperature and Pressure, stands for: T =0°C and P =1atm. Note also that 1L=1000cm3=10-3m3.**The Boltzmann Constant**The ideal gas law becomes: where k =1.38×10-23J/K is the Boltzmann constant.**R or k?**Most physics textbooks use PV=NkT, it does not involves the concept of moles, which is a human creation. However, since your textbook uses R extensively, I will follow suit.**When n is constant**Suppose we change the state of a gas while keeping the total amount of gas the same, we have: This equation is very useful in figuring out the final state of the system.**Example: Compressing gas**A typical engine compresses the gas to 1/9 of its original volume. Given the original pressure is 1atm and the initial temperature is 27°C, if the pressure after compression is 21.7atm, find the temperature of the compressed gas.**Example**Final Initial**Example: Scuba Tank**A scuba tank contains 11L of air at 21°C and 1atm. When the tank is filled with hot air, the temperature is 42°C and the pressure is 2.1×107Pa. What mass of air was added? [Molar mass of air: 28.8g/mol, 1atm=1.013×105Pa]**Degrees of freedom and Equipartition of energy**The result is part of a more general result called the equipartition of energy, which states that each degree of freedom gives rise to a contribution of (1/2)kT per particle. A degree of freedom is each term that appears as x2 or p2 in the energy of the particle, or you can think of it as the number of ways each particle can move.**Counting Degrees of Freedom**Air at room temperature has f=5.

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