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Ideal Gas Law

Ideal Gas Law. Physics 313 Professor Lee Carkner Lecture 10. Exercise #9 -- Chicken. Cool to -2.8C: Q 1 = cm D 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:

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Ideal Gas Law

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  1. Ideal Gas Law Physics 313 Professor Lee Carkner Lecture 10

  2. Exercise #9 -- Chicken • Cool to -2.8C: • Q1 = cmDT = (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

  3. 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

  4. 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

  5. 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:

  6. 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]

  7. Ideal Gas Relations • For an ideal gas: PV = nRT • Internal energy is a function of the temperature only

  8. 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

  9. 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)

  10. Gas Mixtures • e.g. air • How is P,V and T for the mixture related to the properties of the individual gasses?

  11. Mixture Laws • Dalton’s Law: Pm = S Pi (Tm,Vm) • Amagat’s Law: Vm = S Vi(Tm,Pm) • Strictly true only for ideal gases

  12. Mixture Properties Zm = S yiZi • Where yi is the mole fraction (yi = ni/nm) PmVm = ZmnmRTm • It may be hard to determine Zi

  13. First Law for Ideal Gas dU = dQ + dW dW = -PdV • At constant volume: • Since U depends only on T: dQ = CVdT + PdV

  14. Constant Pressure PV = nRT dQ = CVdT + nRdT -VdP • At constant pressure: • Molar heat capacity: cP = cV + R

  15. Forms of the First Law • For an ideal gas: dU = dQ = dQ = dQ =

  16. Heat Capacities • For an ideal gas: • For monatomic gas: • For any gas:

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