Temperature and Ideal Gases

Question 1

What is temperature

Answer 1

It is the measure of the average kinetic energy of molecules in a body

Question 2

What is thermal equilibrium

Answer 2

2 bodies in thermal contact are said to be in thermal equilibrium when there is no net flow of heat from one body to another. It also implies that the 2 bodies are at the same temperature

Question 3

What is a thermometric property

Answer 3

It is a physical property that increases or decreases continuously with temperature

Question 4

What is a fixed point

Answer 4

A fixed point is a temperature that is easily and precisely reproducible where all thermometers show the same reading under the same conditions

Question 5

What is a numerical scale

Answer 5

By taking the value of the thermometric property at the fixed points and dividing the range of values into a number of equal units between the 2 points, we can set up a empirical scale of temperature for that thermometer

Question 6

What is the Thermodynamic Temperature Scale

Answer 6

It is the scale that is theoretical and independent of the property of any particular substance

Question 7

What are the fixed points on the Thermodynamic Temperature Scale

Answer 7

1. Absolute zero (0k)
   
   • all substances have minimum internal energy
   • pressure of an ideal gas becomes 0
2. Triple point of water (273.16k)
   
   • the temperature at which the 3 phases of water coexist in dynamic equilibrium

Question 8

What are the reasons for using triple point of water

Answer 8

1. Unique invariant and occurs at only one temperature and presure
2. The conditions can be easily reproduced using a triple point cell

Question 9

What is the definition of kelvin

Answer 9

1 kelvin is defined to be 1/273.16 of the thermodynamic temperature of the triple point of water

Question 10

What is celsius

Answer 10

θ/C = T/K - 273.15

Question 11

What is the ideal gas equation

Answer 11

pV = nRT

Question 12

What is an ideal gas

Answer 12

An ideal gas is one that obeys the equation pV = nRT at all pressure, volumes and temperatures

Question 13

What is the Boltzmann constant, k

Answer 13

k = R/(Avogadro constant) = 1.38 x 10^-23 JK^-1

pV = NkT

Question 14

What are the assumptions of the kinetic theory for ideal gas

Answer 14

1. A gas consists of a very large number of molecules
2. The gas molecules are in constant random motion and obey the laws of classical mechanics
3. The molecules of the gas make perfect elastic collisions with one another and with the walls of the container
4. The intermolecular forces are negligible except during the time of condition which is compared to the time between collisions
5. Volume of the molecules is negligible compared to the volume of the gas

Question 15

Derivation of the equation p = 1/3(Nm/V)

Answer 15

1. Resolve the motion of molecules along the x-y-z directions
   
   • c^2 = u^2 + v^2 + w^2
2. Find the change of momentum upon collision with a wall
   
   • Consider velocity, u, along x axis
     
     • momentum before collision with wall, p=mu
   • The molecule collides elastically with the wall and rebounds with velocity of -u
   • momentum of collision p=-mu
   • change in momentum, Δp=-2mu
3. Find the force on the wall due to the bombardments of molecules on the wall
   
   • Time between collisions, Δt = 2l/U
   • Rate of change of momentum = -mu^2/l
   • Force exerted by wall on molecule = -mu^2/l
   • By N3L, force on wall by molecule = mu^2/l
   • Consider <u> = mean square velocity in x-direction
     </u>
     • total force on wall = (Nm<u>)/l</u>
4. Find pressure on the wall
   
   • p = (Nm<u>)/V</u>
5. Express in terms of mean-squared speed c
   
   • 1/3 () = <u> = =</u>
   • p = 1/3 (Nm/v) ()
   • p = 1/3 (ρ)()</u></u></u></u>

Question 16

What is the average K.E. of a gas molecule

Answer 16

3/2(kT)

Question 17

What is the total K.E. of N gas molecules

Answer 17

3/2 NkT = 3/2 nRT = 3/2 pV

Question 18

What is the root-mean square speed

Answer 18

crms = (3kT/m)^1/2