14-Simple Models of Matter

Question 1

What is Boyle’s law?

Answer 1

Provided the temperature and the amount of gas remain constant, the pressure is inversely proportional to the volume of gas

Question 2

Using pV = nRT, why is the pressure inversely proportional to the volume?

Answer 2

When the volume is decreased, the molecules collide more frequently with the walls, therefore the pressure is increased. pV is constant

Question 3

If the volume and number of molecules is kept constant, explain why pressure is proportional to the absolute temperature of the gas

Answer 3

P/T = nR/V, which is constant. When the temperature is increased the molecules have more kinetic energy so collide with the walls of the container more frequently, increasing the pressure

Question 4

Why is the volume of a gas proportional to the absolute temperature, if the pressure and number of molecules is kept the same?

Answer 4

Increase in temp causes molecules to have more energy so collide with the walls of the container more frequently and harder, and in order to keep the pressure the same, the volume of the container increases.

Question 5

Why is pressure proportional to the number of molecules, if the volume and temperature are kept the same?

Answer 5

When the number of molecules increases, the frequency of wall collisions increases

Question 6

What are the 2 ways to double the gas pressure?

Answer 6

Double the value of N, or half the volume

Question 7

What is the amount law?

Answer 7

That the pressure of a gas in proportional to the number of molecules

Question 8

What happens to Boyle’s law when real gases are greatly compressed?

Answer 8

It no longer holds, as gas molecules interact with each other, reducing the space in which molecules can move

Question 9

What is an ideal gas?

Answer 9

A gas in which the molecules do not interact at all, and are so tiny that they occupy negligible volume

Question 10

What is Charles’ Law?

Answer 10

That the volume of a gas is proportional to the temperature

Question 11

What is the pressure law?

Answer 11

That the pressure is proportional to the temperature of the gas

Question 12

What is the ideal gas law?

Answer 12

That pV = NkT or pV = nRT

Question 13

What happens to real gases at low temperatures?

Answer 13

They cool into a liquid

Question 14

What 3 assumptions do we have to make in the analysis of the kinetic model of an ideal gas?

Answer 14

• Molecules do not interact at all
• Volume occupied by the gas is negligible
• All collisions are perfectly elastic, so no energy is lost in collisions

Question 15

When a molecule hits the wall of a container, what is the change in its momentum?

Answer 15

-2mc

Question 16

What are the RAVED assumptions made in the kinetic theory of gases?

Answer 16

R-Random motion
A-No attraction between particles
V-Volume of particles is negligible
E-Elastic collisions
D-Duration of collisions is very short

Question 17

What is the equation of pressure?

Answer 17

Force / Area

Question 18

As force is change in momentum / time, what force does a particle exert on the wall of a container?

Answer 18

2mc / t = 2mc / (2x/c) = mc^2 / x

Question 19

What is the pressure exerted by a particle equal to?

Answer 19

mc^2 / Volume

Question 20

What does the total pressure of a gas in a container equal?

Answer 20

1/3 Nmc^2 / V

Question 21

What is the root mean squared speed equation?

Answer 21

As pV = 1/3Nmc^2 and pV = NkT, the root mean squared speed = root (3kT / m)

Question 22

What does the average kinetic energy of particles equal?

Answer 22

1/2 mc^2 = 3/2 kT

Question 23

Why is the displacement of a random molecule hard to predict?

Answer 23

Because each collision chnages the direction of a molecule in a random way

Question 24

On average, if a molecule makes N steps, what distance will it reach from its starting point?

Answer 24

Mean free path X A distance of root N metres

Question 25

What is the mean displacement of all the molecules?

Answer 25

0, but some will travel a great distance

Question 26

Why does a gas diffuse 5 cm in 10 seconds, but takes more than 100 times as long to diffuse 500 cm?

Answer 26

Qualitatively, in a short time interval, most steps take a molecule away from the source. In a long time interval, a greater proportion of steps takes the molecule back towards the source.
Quantitatively, D = √N d. When D is increased by a factor of 100, √N must be increased by a factor of 100, so N is increased by a factor of 10 000, hence takes much longer.

Question 27

What is the internal energy of a system U?

Answer 27

The sum of the random potential and kinetic energy of its molecules

Question 28

What is the first law of thermodynamics?

Answer 28

Change in internal energy U = Work done on system W + energy transferred thermally to system Q

Question 29

Why does the temperature of a trapped volume of gas rise when the gas is compressed (as in the case of a bicycle pump)?

Answer 29

ΔU = Q + W. Work is being done ON the gas by compressing it (work done = force x distance), so W is positive. If no thermal energy enters or leaves the system (Q = 0), then ΔU = W = a positive number. As internal energy U is proportional to temperature, a positive ΔU means an increase in temperature

Question 30

What does the change in internal energy equal in terms of the specific heat capacity?

Answer 30

Change in internal energy = mass x specific heat capacity X change in temp