Thermal Properties of Matter Flashcards
What is the ideal gas equation?
pV = nRT, where p is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant and T is the temperature in Kelvin.
State the value of the ideal gas constant.
8.31 J mol^-1 K^-1
What is the alternative to the ideal gas equation?
pV = NkbT, where N is the number of atoms, kb is Boltzmanns constant and T is the temperature in K.
What is Van der Waal’s equation?
(p + an^2/V^2)(V-n*b) = nRT, where a and b are empirical constants that are different for each gas.
How do you work out the pressure on one surface considering a container of volume V filled with an ideal gas, with N gas molecules each of mass m and average velocity v.
- Square with surface area A
- Total change in momentum is 2mv x
- Number of collisions in time t is 1/2*N/V * Av x dt
- Total change in momentum is number of collisions times the change in momentum
- Force is rate of change of momentum so divide by dt
- Pressure is force/area
How do you work out the velocity of atoms in the container using the equation you found for pressure?
- No preferred direction so v x = v y = v z, so v^2 = each velocity component squared and added together
- v rms = sqrt(v^2), so v rms = 3v x^2, so pV = 1/3 * Nmv rms
- N1/2mv^2 = KE - substitute this in
- Then use pV = NkbT and pV = nRT with other equations to get expressions for the rms speed
What does the Maxwell Boltzmann distribution show?
The distribution of speeds of molecules in a gas.
Describe the Maxwell Boltzmann distribution diagram for 3 different temperatures each hotter than the last.
- dN on y axis and velocity on x-axis
- the larger the temperature, the smaller the peak of the graph is and the further along the x-axis it is (the most probable speed)
What does it mean if the behaviour of a gas is ballistic or diffusive?
Ballistic - behaviour dominated by when gas molecules hit the walls
Diffusive - behaviour of gas determined by collisions between gas molecules
What determines whether a gas is ballistic or diffusive?
The mean free path (average distance between collisions).
What is the condition for a collision between 2 molecules of radius r? What is the collisions volume?
They’ll collide if within 2r of another gas molecule. Each molecule sweeps out a collision volume of pi*(2r)^2 * v dt
How do you use the collision volume to work out the collision rate of molecules?
- Number of collisions is the number of molecules in the collision volume : dn/dt = 4pir^2 * N/V * v
- Relative speed between two gas molecules is sqrt(2)*v rms
- Collision rate dn/dt = 4pir^2 * N/V * sqrt(2) * v rms
What is the mean time τ between collisions of molecules in a gas, considering the collision rate?
τ = (dn/dt)^-1 = V/(4pir^2 * sqrt(2)*v rms * N)
What is the mean free path, considering the mean time between collisions?
τ * v rms = V/ (sqrt(2) * 4pir^2 * N)
Can substitute in pV = NkbT
What is heat capacity?
The amount of heat energy required to increase the temperature of a substance by 1 K.
