14-Simple Models of Matter Flashcards
What is Boyle’s law?
Provided the temperature and the amount of gas remain constant, the pressure is inversely proportional to the volume of gas
Using pV = nRT, why is the pressure inversely proportional to the volume?
When the volume is decreased, the molecules collide more frequently with the walls, therefore the pressure is increased. pV is constant
If the volume and number of molecules is kept constant, explain why pressure is proportional to the absolute temperature of the gas
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
Why is the volume of a gas proportional to the absolute temperature, if the pressure and number of molecules is kept the same?
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.
Why is pressure proportional to the number of molecules, if the volume and temperature are kept the same?
When the number of molecules increases, the frequency of wall collisions increases
What are the 2 ways to double the gas pressure?
Double the value of N, or half the volume
What is the amount law?
That the pressure of a gas in proportional to the number of molecules
What happens to Boyle’s law when real gases are greatly compressed?
It no longer holds, as gas molecules interact with each other, reducing the space in which molecules can move
What is an ideal gas?
A gas in which the molecules do not interact at all, and are so tiny that they occupy negligible volume
What is Charles’ Law?
That the volume of a gas is proportional to the temperature
What is the pressure law?
That the pressure is proportional to the temperature of the gas
What is the ideal gas law?
That pV = NkT or pV = nRT
What happens to real gases at low temperatures?
They cool into a liquid
What 3 assumptions do we have to make in the analysis of the kinetic model of an ideal gas?
- 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
When a molecule hits the wall of a container, what is the change in its momentum?
-2mc
What are the RAVED assumptions made in the kinetic theory of gases?
R-Random motion A-No attraction between particles V-Volume of particles is negligible E-Elastic collisions D-Duration of collisions is very short
What is the equation of pressure?
Force / Area
As force is change in momentum / time, what force does a particle exert on the wall of a container?
2mc / t = 2mc / (2x/c) = mc^2 / x
What is the pressure exerted by a particle equal to?
mc^2 / Volume
What does the total pressure of a gas in a container equal?
1/3 Nmc^2 / V
What is the root mean squared speed equation?
As pV = 1/3Nmc^2 and pV = NkT, the root mean squared speed = root (3kT / m)
What does the average kinetic energy of particles equal?
1/2 mc^2 = 3/2 kT
Why is the displacement of a random molecule hard to predict?
Because each collision chnages the direction of a molecule in a random way
On average, if a molecule makes N steps, what distance will it reach from its starting point?
Mean free path X A distance of root N metres
What is the mean displacement of all the molecules?
0, but some will travel a great distance
Why does a gas diffuse 5 cm in 10 seconds, but takes more than 100 times as long to diffuse 500 cm?
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.
What is the internal energy of a system U?
The sum of the random potential and kinetic energy of its molecules
What is the first law of thermodynamics?
Change in internal energy U = Work done on system W + energy transferred thermally to system Q
Why does the temperature of a trapped volume of gas rise when the gas is compressed (as in the case of a bicycle pump)?
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
What does the change in internal energy equal in terms of the specific heat capacity?
Change in internal energy = mass x specific heat capacity X change in temp
