# Thermodynamics and Ideal Gas

Topics: Thermodynamics, Entropy, Energy Pages: 24 (5879 words) Published: February 3, 2013
Thermodynamics Exam Prep 2012
Chapter 1: Basic and Ideal Gas Law
1.1 State of a System
System + surroundings = Universe
Open system: can exchange matter and energy with the surroundings Closed system: can exchange energy with the surroundings
Isolated system: cannot exchange matter or energy with the surroundings If one knows the x/y/z position and the vx/vy/vz velocity of a particle (6 parameters) for a time point t0 it is possible to predict where the particle will be for any future time point and to determine the previous particle positions for any time point in the past. For many particles, it is necessary to know the 6 parameters for each gas particles, therefore 6xN parameters to know the previous and past positions of all these gas particles. Volume

Symbol: V
Units: L
1L = 10-3m3
1000mL = 1L
1000µL = 1mL
Temperature
Symbol: T
Units: K
ºC K = +273
Pressure
Symbol: P
Units: force/area 1Pa = 1 Nm-2
105 Pa = 1 Bar
101300 Pa = 101.3kPa = 1.013 Bar = 1 atm = 760mmHg = 760 Torr *using the SI units on the left hand side will force SI units on the right hand side Where does gas pressure come from?
Gas molecules are in constant chaotic motion which results in frequent collisions with walls. Momentum transfer tends to ‘bulge out’ the container walls. How Can We Manage Gas Pressure?
Many pressure gauges use a spring-loaded system to provide a certain counter-pressure. Example:
What is the height of the Hg column when the external pressure is patm = 101.3kPa? *density of Hg(l) = 13.59gcm-3
ph = dgh
Height of column:
Ph = Patm
dgh = Patm
h = Patm/dg
= 101.3kPa/(13.59gcm-3)(9.81ms-2)
= 0.76m
1.2 Intensive and Extensive Variables
Intensive Variables: independent of the size of the system (pressure, temperature, density) Extensive Variables: depend on the size of the system (volume, mass, internal energy, entropy, moles) The ratio of 2 extensive variables is usually intensive:

Density = mass/volume
n=NNA where NA = 6.022 x 1023 mol-1 = Avogadro’s number
Vm=Vn= molar volume
Vm is intensive because volume and number of moles are extensive.

1.3 Ideal Gas Law, Temperature
Heat is related to the speed of molecular movement (translational, vibrational, rotational) Hot = fast, cold = slow
TRANSLATIONAL: the movement of the particles in random ways, hot will move further/quicker than slow particles VIBRATIONAL: a hot set of particles will have more vibration, therefore affecting more particles than a cold set. ROTATIONAL: energy will rotate through hot particles quicker than it will rotate through cold particles **At T=0K, all motion seizes

There are 3 mechanisms by which heat can be transferred:
Conduction: spreading of vibrational motions (ie. Heat being transferred down a metal rod covered with pieces of candle wax and eventually each piece of candle wax melting, starting with the closest to the heat source) Convection: movement of hot material (ie. One flame in the middle of the room, the heat will rise and spread throughout the entire room) Radiation: hot molecules emit electromagnetic radiation, which cold molecules absorb. When 2 closed systems that can exchange heat are brought into contact with each other, they will exchange heat until they have both reached the same temperature (Thermal equilibrium) Zeroth Law of Thermodynamics:

If system A is in thermal equilibrium with B, and system B is in thermal equilibrium with C, then A is also in thermal equilibrium with C. ** in equilibrium, there is no net change, however many processes are still occurring it’s just that and are equal Ideal Gas Law:

pV = nRT
Ideal means we assume that:
1. Molecules do not interact with eachother
2. Individual gas molecules have 0 volume
Using molar volume, the ideal gas law is:
pVm = RT
T = pVm/R
Example:
Calculate Vm for an ideal gas under standard temperature and pressure conditions: 0ºC and 100kPa p•Vm = RT
Vm = RT/P
= (8.31J/Kmol•273K)/105N/m2
= 0.0227m3mol-1
* p...