Ideal Gas Law Physics 313 Professor Lee Carkner Lecture 10

Exercise #9 -- Chicken  Cool to -2.8C:  Q 1 = cm  T = (3.32)(50)(8.8) =  Phase change:  Q 2 = Lm = (247)(5) =  Cool to -18 C:  Q 3 = (1.77)(50)(15.2) =  Cool box to -18 C:  Q 4 = (1.4)(1.5)(24) =  Sum all heats:  Q T = Q 1 + Q 2 + Q 3 + Q 4 =  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 (V C,P C,T C )

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:   P m =  P i (T m,V m )  Amagat’s Law:  V m =  V i (T m,P m )  Strictly true only for ideal gases

Mixture Properties  Z m =  y i Z i  Where y i is the mole fraction (y i = n i /n m )  P m V m = Z m n m RT m  It may be hard to determine Z i

First Law for Ideal Gas dU = dQ + dW dW = -PdV   At constant volume:  Since U depends only on T: dQ = C V dT + PdV

Constant Pressure PV = nRT dQ = C V dT + nRdT -VdP  At constant pressure:  Molar heat capacity: c P = c V + R

Forms of the First Law  For an ideal gas: dU = dQ =

Heat Capacities  For an ideal gas:   For monatomic gas:  For any gas: