9 - Ideal Gases

9 - Ideal Gases - Molecules in Motion Kinetic Theory of...

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1 Molecules in Motion Kinetic Theory of Gases
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2 Objective: Understand the origins of the IDEAL GAS LAW IDEAL GAS LAW: PV = nRT P = Pressure V = Volume n = # moles R = ideal gas constant = 8.314 Joules Kelvin -1 Mol -1 T = Temperature The Ideal Gas Law - first written in 1834 by Emil Clapeyron (shown here relaxing at home)
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3 1. An ideal gas consists of discrete particles (could be molecules or atoms). 2. The particles are far apart and occupy zero volume. 3. The particles are in constant motion – Newtonian type physics describes those motions 4. The particles couldn’t could care less about each other or the container that holds them (no attractive forces). 5. The particles do collide with one another and the sides of the container. 6. Energy is conserved. A particle may gain energy if another loses an equal amount . The Kinetic Theory of Ideal Gases - Assumptions
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4 1. An ideal gas consists of discrete particles (could be molecules or atoms). 2. The particles are far apart and occupy zero volume. 3. The particles are in constant motion – Newtonian type physics describes those motions 4. The particles couldn’t care less about each other or the container that holds them (no attractive forces). 5. The particles collide with one another and the sides of the container. 6. Energy is conserved. A particle may gain energy if another loses an equal amount . The Kinetic Theory of Ideal Gases - Assumptions
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5 A few things to remember: k B T= an energy ± each degree of freedom in a particle contains ½k B T of energy (3/2 k B Ttotal ± WHY?? ) Momentum = mv = (mass)(velocity) d(mv)/dt = a Force = ' p/ ' T ( p = momentum) Force/Area, or Force per unit Area = Pressure h = 6.626e-34 J·s (kg m 2 s -1 ) = Planck’s constant k B = 1.381e-23 J·K -1 T = temperature (in K)
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6 Particle of mass m striking a wall within a container. With the below assumptions, what does the above picture imply? Particles move Particles move Particles collide Energy is conserved Newtonian physics is good. Redacted Assumptions
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7 Particle has momentum ( p ) = mass × velocity (= mv x ) before striking wall = -mv x after striking wall The particles move They collide They collide (with walls) Energy is conserved Energy is conserved Newtonian physics is good. Redacted Assumptions ' p= 2m ' v = 2m|v x | (moving in x-direction) What is momentum change upon collision?
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8 ' p= 2m ' v = 2m|v x | How about per unit time? Unit time = ' t Distance particle travels in ' t= |v x | ' t The particles move They collide Energy is conserved Newtonian physics is good. Redacted Assumptions
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9 The particles move They collide Energy is conserved Newtonian physics is good. Redacted Assumptions ' p= 2m ' v = 2m|v x | Volume containing all striking particles Distance particle travels ' t= |v x | ' t Wall area = A |v x |A ' t= a Volume element containing all particles that might strike the wall within ' t v x ' t
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10 The particles move They collide Energy is conserved Newtonian physics is good.
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This note was uploaded on 11/10/2011 for the course CH 1b taught by Professor Natelewis during the Winter '09 term at Caltech.

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9 - Ideal Gases - Molecules in Motion Kinetic Theory of...

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