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: