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Kinetic Theory of Gases

Kinetic Theory of Gases. Physics 313 Professor Lee Carkner Lecture 11. Exercise #10 Ideal Gas. 8 kmol of ideal gas Compressibility factors Z m = S y i Z i y CO2 = 6/8 = 0.75 V = ZnRT/P = (0.48)(1.33) = 0.638 m 3 Error from experimental V = 0.648 m 3 Compressibility factors: 1.5%

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Kinetic Theory of Gases

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  1. Kinetic Theory of Gases Physics 313 Professor Lee Carkner Lecture 11

  2. Exercise #10 Ideal Gas • 8 kmol of ideal gas • Compressibility factors • Zm = SyiZi • yCO2 = 6/8 = 0.75 • V = ZnRT/P = (0.48)(1.33) = 0.638 m3 • Error from experimental V = 0.648 m3 • Compressibility factors: 1.5% • Most of the deviation comes from CO2

  3. Ideal Gas • At low pressure all gases approach an ideal state • The internal energy of an ideal gas depends only on the temperature: • The first law can be written in terms of the heat capacities: dQ = CVdT +PdV dQ = CPdT -VdP

  4. Heat Capacities • Heat capacities defined as: CV = (dQ/dT)V = (dU/dT)V • Heat capacities are a function of T only for ideal gases: • Monatomic gas • Diatomic gas g = cP/cV

  5. Adiabatic Process • For adiabatic processes, no heat enters of leaves system • For isothermal, isobaric and isochoric processes, something remains constant

  6. Adiabatic Relations dQ = CVdT + PdV VdP =CPdT (dP/P) = -g (dV/V) . • Can use with initial and final P and V of adiabatic process

  7. Adiabats • Plotted on a PV diagram adibats have a steeper slope than isotherms • If different gases undergo the same adiabatic process, what determines the final properties?

  8. Ruchhardt’s Method • How can g be found experimentally? • Ruchhardt used a jar with a small oscillating ball suspended in a tube

  9. Finding g • Also related to PVg and Hooke’s law • Modern method uses a magnetically suspended piston (very low friction)

  10. Microscopic View • Classical thermodynamics deals with macroscopic properties • The microscopic properties of a gas are described by the kinetic theory of gases

  11. Kinetic Theory of Gases • The macroscopic properties of a gas are caused by the motion of atoms (or molecules) • Pressure is the momentum transferred by atoms colliding with a container

  12. Any sample has large number of particles (N) Atoms have no internal structure No forces except collision Atoms distributed randomly in space and velocity direction Atoms have speed distribution Assumptions

  13. Particle Motions • The pressure a gas exerts is due to the momentum change of particles striking the container wall • We can rewrite this in similar form to the ideal equation of state: PV = (Nm/3) v2

  14. Applications of Kinetic Theory • We then use the ideal gas law to find T: PV = nRT T = (N/3nR)mv2 • We can also solve for the velocity: • For a given sample of gas v depends only on the temperature

  15. Kinetic Energy • Since kinetic energy = ½mv2, K.E. per particle is: • where NA is Avogadro’s number and k is the Boltzmann constant

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