Chapter 18. System: an object under consideration, an example we will use often is a box of gas. State variables: variables that give us information about.

Thermal Properties of Matter

Thermal Properties of MatterChapter 18State of a SystemSystem: 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=nRTThe Ideal Gas LawIdeal 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 =0C and P =1atm.Note also that 1L=1000cm3=10-3m3.The Boltzmann constant

The Boltzmann Constant

The ideal gas law becomes:

where k =1.3810-23J/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 constantSuppose 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 gasA typical engine compresses the gas to 1/9 of its original volume. Given the original pressure is 1atm and the initial temperature is 27C, if the pressure after compression is 21.7atm, find the temperature of the compressed gas.

Example: Scuba TankA scuba tank contains 11L of air at 21C and 1atm. When the tank is filled with hot air, the temperature is 42C and the pressure is 2.1107Pa. What mass of air was added?[Molar mass of air: 28.8g/mol, 1atm=1.013105Pa]

Van Der Waals Equation

No need to memorize. The van der Waals equation is a slightly better approximation than the Idea Gas Law. It accounts for the intermolecular forces and the volume of the gas molecules themselves. It also gives an indication of phase transition.Kinetic-molecular Model of a gas

First assume all particles have the same speed, half are moving toward the wall, half moving away. We want to figure out the force on the wall due to the collision of the gas.

Predict the pressure

Temperature and KE

RMS Velocity

15Mean vs rms

16Example: RMS speed of hydrogenWhat is the rms speed of a hydrogen molecule at STP? Molecular mass: 2g/mol

STP: Standard temperature & pressureT=0oC=273K, P=1atm=105Pa

17Degrees of freedom and Equipartition of energyThe 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.

Degrees of Freedom for Diatomic molecules

Counting Degrees of FreedomTypes of gasTranslational DFRotational DFVibrational DFTotal DF (f)Monatomic(all temperature)3003Diatomic(low temperature)3003Diatomic(medium temperature)3205Diatomic (high temperature)3227Polyatomic (low temperature)3306Polyatomic (high temperature)33VariesVariesAir at room temperature has f=5.Energy of a gas

What happens to U when T is changed?

How much U is needed to change T by one unit? (This is the total heat capacity only when there is no work W)

Molar heat capacity

Phases of Matter