Physics 1210/1310 Mechanics&Thermodynamics Lecture 39~40 Thermodynamics.
Physics 114 – Lecture 39
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Transcript of Physics 114 – Lecture 39
L39-s1,8
Physics 114 – Lecture 39• §13.6 The Gas Laws and Absolute Temperature
• Boyle’s Law: (~1650) − For a sample of gas, for which T = const, V 1/P or
• PV = const
• Effect of Temperature?
• Charles’ Law: (~1780) – For a sample of gas,
• for which P = constant, V T, if we
redefine the origin of T → T(K) = T(0C) + 273.15 – absolute or Kelvin scale
L39-s2,8
Physics 114 – Lecture 39• Gay-Lussac’s Law: (~1820) − For a sample of gas,
for which V = const, P T, where T is in kelvins (K)• Study Example 13.9• §13.7 The Ideal Gas Law• PV T• Amount of gas? Expt.: if P and T are const, V m • PV mT• Constant? → PV = α RT, where α depends on m• It turns out that α is conveniently expressed in moles
L39-s3,8
Physics 114 – Lecture 39
• E.g., the number of moles in 96.0 g of O2 for which the molecular mass is 2 X 16.0 = 32.0
• The Ideal Gas Law then becomes,• PV = nRT where R = 8.314 J/(mol. K)
where R is the universal gas const and is the same for
all gases
)(grams/mol massmolecular
(grams) mass (mol)n
mol 3.00 g/mol 32.0
g 96.0 n
L39-s4,8
Physics 114 – Lecture 39• Reminder: P is the absolute pressure and T, the
temperature, is measured in kelvins• Of course real gases, as opposed to ideal gases,
follow this law only when they are neither at very high pressures nor near their liquefaction point
• §13.8 Problem Solving with the Ideal Gas Law• Study Problems 13.10, 13.11, 13.12 and 13.13
L39-s5,8
Physics 114 – Lecture 39• §13.9 Ideal Gas Law in Terms of Molecules:
Avogadro’s Number• Avogadro’s Hypothesis: Equal volumes of gas at the
same temperature and pressure contain equal numbers of molecules
• This is consistent with R being the same for all gases• Thus: PV = nRT states that, if P, V and T are the
same for samples of two different gases, then n must be the same for these gases since R has the same value for all gases and the number of molecules in 1 mole is the same for all gases
L39-s6,8
Physics 114 – Lecture 39• The number of molecules in one mole of any pure
substance is given by Avogadro’s number, NA
• The accepted value is:• NA = 6.02 X 1023 molecules/mole• We have PV = nRT =
• which may be written, PV = N k T • where
• and where k is known as the Boltzmann constant
RT N
N
A
J/K 10 1.38 mol / 10 6.02
J/(mol.K) 8.314
N
R k 23-
23A
L39-s7,8
Physics 114 – Lecture 39• §13.10 Kinetic Theory and the Molecular Interpretation of
Temperature• Assumptions:• 1. Large number of mols each of
of mass, m, moving randomly• 2. Mols on average far apart wrt
their diameter – force between mols = 0,unless they are colliding
• 3. Mols interact only when they collide andfollow laws of classical mechanics
• 4. Collisions with the container wallsare elastic and of short duration,compared with time between collisions
L39-s8,8
Physics 114 – Lecture 39• Consider one molecule colliding
with the wall
Δp1 = -mv1x – (mv1x) = -2 mv1x for mol
Δt = 2l/v1x
F1 = Δp1/Δt = -2mv1x/ (2l/v1x) = -mv1x2/l
For N molecules, total force on wall
F = (m/l) (v1x2 + v2x
2 + v3x2 + … + vNx
2)
Since v1x2 + v2x
2 + v3x2 + … + vNx
2 = N (vx2)ave
F = (m/l) N (vx2)ave
With (vx2)ave = v2
ave /3 → P = F/A = ⅓ Nm v2ave /(Al)
With V = Al → PV = ⅓ Nm v2ave = ⅔ N(½ mv2
ave) = ⅔ N KEave
Comparing with PV = NkT → KEave = ½ mv2ave = (3/2) kT
Thus T is a measure of KEave of the molecules in the sample
vx
-vx
x
l