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Kinetic Theory of Gases I

Ideal Gas

The number of molecules is large

The average separation between molecules

is large

Molecules moves randomly

Molecules obeys Newtons Law

Molecules collide elastically with each

other and with the wall

Consists of identical molecules

The Ideal Gas Law

R the Gas Constant R 8.31 J/mol K

Pressure and Temperature

Pressure Results from collisions of molecules

on the surface

Only molecules moving toward the surface hit the

surface. Assuming the surface is normal to the x

axis, half the molecules of speed vx move toward

the surface.

Only those close enough to the surface hit it in

time dt, those within the distance vxdt

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Pressure ? Density x Kinetic Energy

Temperature ? Kinetic Energy

Internal Energy

For monatomic gas the internal energy sum of

the kinetic energy of all molecules

HRW 16P (5th ed.). Consider a given mass of an

ideal gas. Compare curves representing

constant-pressure, constant volume, and

isothermal processes on (a) a p-V diagram, (b) a

p-T diagram, and (c) a V-T diagram. (d) How do

these curves depend on the mass of gas?

HRW 18P (5th ed.). A sample of an ideal gas is

taken through the cyclic process abca shown in

the figure at point a, T 200 K. (a) How many

moles of gas are in the sample? What are (b) the

temperature of the gas at point b, (c) the

temperature of the gas at point c, and (d) the

net heat added to the gas during the cycle?

(d) Cyclic process ? ?Eint 0

Volume (m3)

Q W Enclosed Area 0.5 x 2m2 x 5x103Pa 5.0

x 103 J

HRW 30E (5th ed.).(a) Compute the

root-mean-square speed of a nitrogen molecule at

20.0 C. At what temperatures will the

root-mean-square speed be (b) half that value and

(c) twice that value?

HRW 34E (5th ed.). What is the average

translational kinetic energy of nitrogen

molecules at 1600K, (a) in joules and (b) in

electron-volts?

(b) 1 eV 1.60 x 10-19 J

Kinetic Theory of Gases II

Mean Free Path

- Molecules collide elastically with other molecules

Mean Free Path l average distance between two

consecutive collisions

Molar Specific Heat

Definition

Constant Volume

(Monatomic)

Constant Pressure

(Monatomic)

Adiabatic Process

1st Law

Ideal Gas Law

(Q0)

Divide by pV

Ideal Gas Law

Equipartition of Energy

The internal energy of non-monatomic molecules

includes also vibrational and rotational energies

besides the translational energy.

Monatomic Gases

3 translational degrees of freedom

Diatomic Gases

3 translational degrees of freedom

2 rotational degrees of freedom

2 vibrational degrees of freedom

HOWEVER, different DOFs require

different temperatures to excite. At room

temperature, only the first two kinds are excited

HRW 63P (5th ed.). Let 20.9 J of heat be added to

a particular ideal gas. As a result, its volume

changes from 50.0 cm3 to 100 cm3 while the

pressure remains constant at 1.00 atm. (a) By how

much did the internal energy of the gas change?

If the quantity of gas present is 2.00x10-3 mol,

find the molar specific heat at (b) constant

pressure and (c) constant volume.

(a) Constant pressure W p?V

HRW 63P (5th ed.). Let 20.9 J of heat be added to

a particular ideal gas. As a result, its volume

changes from 50.0 cm3 to 100 cm3 while the

pressure remains constant at 1.00 atm. (a) By how

much did the internal energy of the gas change?

If the quantity of gas present is 2.00x10-3 mol,

find the molar specific heat at (b) constant

pressure and (c) constant volume.

HRW 81P (5th ed.). An ideal gas experiences an

adiabatic compression from p 1.0 atm, V 1.0x106

L, T 0.0 C to p 1.0 x 105 atm, V 1.0x103 L.

(a) Is the gas monatomic, diatomic, or

polyatomic? (b) What is its final temperature?

(c) How many moles of gas are present? (d) What

is the total translational kinetic energy per

mole before and after the compression? (e) What

is the ratio of the squares of the rms speeds

before and after the compression?

Monatomic

HRW 81P (5th ed.). An ideal gas experiences an

adiabatic compression from p 1.0 atm, V 1.0x106

L, T 0.0 C to p 1.0 x 105 atm, V 1.0x103 L.

(a) Is the gas monatomic, diatomic, or

polyatomic? (b) What is its final temperature?

(c) How many moles of gas are present? (d) What

is the total translational kinetic energy per

mole before and after the compression? (e) What

is the ratio of the squares of the rms speeds

before and after the compression?

HRW 81P (5th ed.). An ideal gas experiences an

adiabatic compression from p 1.0 atm, V 1.0x106

L, T 0.0 C to p 1.0 x 105 atm, V 1.0x103 L.

(a) Is the gas monatomic, diatomic, or

polyatomic? (b) What is its final temperature?

(c) How many moles of gas are present? (d) What

is the total translational kinetic energy per

mole before and after the compression? (e) What

is the ratio of the squares of the rms speeds

before and after the compression?

HRW 81P (5th ed.). An ideal gas experiences an

adiabatic compression from p 1.0 atm, V 1.0x106

L, T 0.0 C to p 1.0 x 105 atm, V 1.0x103 L.

(a) Is the gas monatomic, diatomic, or

polyatomic? (b) What is its final temperature?

(c) How many moles of gas are present? (d) What

is the total translational kinetic energy per

mole before and after the compression? (e) What

is the ratio of the squares of the rms speeds

before and after the compression?

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