# Ideal gas and kinetic gas theory Boltzmann constant.

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Ideal gas and kinetic gas theory Boltzmann constant

Ideal gas and kinetic gas theory Properties of an ideal gas: 1.Large distances between particles 2.Particles interact only during collisions (hard spheres)

Temperature and average translational kinetic energy Find the average kinetic energy for one nitrogen molecule at room temperature. To which speed does this correspond? How much translational kinetic energy does this molecule have at 0 K? How much energy is stored in this auditorium in translational kinetic energy of the air molecules?

Argon Helium Same kinetic energy, hence What will the ratio of the velocities be after mixing ?

Maxwell velocity distribution 20040060080010001200 Occurrence Speed (m/s) Argon, 300 K V rms =432 m/s V mean =398 m/s V max =353 m/s

Maxwell velocity distribution 20040060080010001200 Occurrence Speed (m/s) Argon, 300 K Neon, 300 K Helium, 300 K

Thermodynamic work and the first law of thermodynamics

Ideal gas p, T, V, n Internal energy U Kinetic energy of particles System Environment

Ideal gas System Environment System Environment dx F=pA

Thermodynamic work –definitions Work is done if the boundary of the system shifts with respect to the environment dV > 0: expansion work by gas on env. dV < 0: compression work on gas by env.

An isobaric process p V Heat Q 1 2 12 Did the temperature change as well? P=1 atm 2L balloon

An isochoric process p V Heat Q 1 2 1 2 Did the temperature change?

An isothermal process p V 1 2 1 2 Ice water Is the work negative or positive? 10% reduction Was there any heat exchange?

Insulation An adiabatic process p V 1 2 1 2 No heat transfer possible

What is a quasistatic process? 1 2 Ice water p V 1 2 Temperature is always equal to the temperature of the bath Thermal equilibrium at all times! = quasistatic = reversible Realistic: it takes time for temperature equilibration – not thermal equilibrium at all times = not quasistatic = irreversible

Processes you should be able to distinguish: Isobaric Isothermal Isochoric Adiabatic Quasistatic Reversible Irreversible

Internal energy Thermal internal energy: part that changes if T changes Can be chemical, nuclear, strain, PE, KE Ideal gas: total KE of all particles Symbol: U Property: characterizes state of system

Internal energy of ideal gas? Monatomic gas: Each particle has 3 degrees of freedom Each degree of freedom has ½ kT of (kinetic) energy on average Diatomic gas: Each molecule has 3 degrees of freedom for translation Each molecule has 2 degrees of freedom for rotation Each molecule has 1 degree of freedom for bond stretching which engages only at very high temperatures Each degree of freedom has ½ kT of (kinetic) energy on average

Example Compare the internal energy of 1 mole of helium and 1 mole of nitrogen at 300 K

First Law of thermodynamics System in state 1: p 1, T 1, V 1, U 1 System in state 2: p 2, T 2, V 2, U 2 process Heat exchange Q Work W Conservation of energy:

Isobaric process p V Heat Q 1 2 12 P=1 atm 2L balloon How much heat transfer was necessary to the 7-L flask of nitrogen in order to inflate the 2-L balloon in an isobaric process?

An isothermal process p V 1 2 1 2 Ice water 10% reduction How much ice has been molten in the ice water during this compression? The flask contains originally 7 L of nitrogen at initially 1 atm.

Adding heat -how much is needed ? Q Q T increases p increases p constant V constant V increases

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