ideal gas law physics 313 professor lee carkner lecture 10
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Ideal Gas Law
Physics 313Professor Lee
CarknerLecture 10
Exercise #9 -- Chicken Cool to -2.8C:
Q1 = cmT = (3.32)(50)(8.8) = Phase change:
Q2 = Lm = (247)(5) = Cool to -18 C:
Q3 = (1.77)(50)(15.2) = Cool box to -18 C:
Q4 = (1.4)(1.5)(24) = Sum all heats:
QT = Q1 + Q2 + Q3 + Q4 = Most heat lost for phase change
Ideal Gas
What is an ideal gas?
The properties converge to common values as P goes to zero
An ideal gas is any gas at the limit of zero pressure
Approaching Zero Pressure
The equation of state of a gas depends on T, P and V
We know that for constant V:
Can express Pv relationship by virial expansion:
Experiment reveals that for constant T:
A is function of T only
Equation of State: Ideal Gas
Combining equations We can write the constant part of
this equation as: The equation of state for any gas
as pressure approaches zero is:
Internal Energy
What does the internal energy depend on?
For a real gas U is dependant on P
(U/P)T = 0 [as P goes to 0]
Ideal Gas Relations
For an ideal gas:PV = nRT
Internal energy is a function of the temperature only
Ideal and Real Gas Real gases deviate from ideal ones with pressure
We can express the deviation from ideal gas behavior with the compressibililty factor, Z
For an ideal gas:Pv = RT
For a real gas:
Pv = ZRT
z = 1 for ideal gasses
Critical Point
What determines if a gas is at high or low pressure?
The point where there is no difference between liquid and gas
The critical point is defined by a critical volume, pressure and temperature (VC,PC,TC)
Gas Mixtures
e.g. air
How is P,V and T for the mixture related to the properties of the individual gasses?
Mixture Laws
Dalton’s Law:
Pm = Pi (Tm,Vm) Amagat’s Law:
Vm = Vi(Tm,Pm) Strictly true only for ideal gases
Mixture Properties
Zm = yiZi
Where yi is the mole fraction (yi = ni/nm)
PmVm = ZmnmRTm
It may be hard to determine Zi
First Law for Ideal Gas
dU = dQ + dWdW = -PdV
At constant volume:
Since U depends only on T:
dQ = CVdT + PdV
Constant PressurePV = nRT
dQ = CVdT + nRdT -VdP
At constant pressure:
Molar heat capacity:
cP = cV + R
Forms of the First Law
For an ideal gas:dU = dQ = dQ = dQ =
Heat Capacities
For an ideal gas: For monatomic gas:
For any gas: