MOaD 3 Flashcards
heat capacity cv (27 cards)
Where can thermal energy be stored?
For a molecule, these storage places are the energy levels for translation, vibration and rotation.
why is electronical energy ignored
for thermal energy to be stored electronically, this requires high energy.
large heat capacity.
The more ways a molecule can move, rotate or vibrate at a certain temperature, the more heat it can store,
The heat capacity, C,
The amount of heat (energy) required to raise the temperature of a body by 1 K.
The molar heat capacity, Cm,
The amount of heat (energy) required to raise the temperature of 1 mol of a substance by 1 K.
The more heat that stored in a body…….
the higher its internal energy, U.
U is a function of what ?
pressure, p, and volume, V, because these parameters affect the ways in which molecules move.
how can C can be measured?
Cp - Keep p constant
CV - Keep V constant
Mathematically, CV, is given by:
𝐶_𝑉=(𝜕𝑈/𝜕𝑇)_𝑉
CVis not as useful as……
Cp
At constant volume, change in internal energy is given by…..
dU = CV.dT, or for large changes:
ΔU = CVΔT = qV
We can measure qV using….
a bomb calorimeter
what kind of bomb calorimeter is used to measure the transfer of energy, qv?
An adiabatic bomb calorimeter.
how is a bomb calorimeter built?
Whole assembly is lagged so the heat generated inside cannot escape, and it’s enclosed in a strong container so that V is fixed
Cv cal
Pass a current, I, through a heater wire for a time, t, and measure the temp rise, ΔT.
1.E = I V t (V here is the voltage!)
2.E = qV = CV cal * ΔT,
finding H
- Burn a known no. moles, n, of the sample in O2.
[No work is done (w = 0) because pΔV =0]
Measure ΔT
ΔU = CVcal* ΔT
Convert ΔU to ΔH
population energy levels and heat
Heating at constant volume changes the population of energy level but not the separation of the levels.
Translation:
Molecules can move in 3D space, i.e. in the x, y and z directions.
Mean translational energy = ½kBT + ½kBT + ½kBT = 3/2kBT
Rotation: Non-linear molecules
can rotate around the x, y and z axes.
Mean rotational energy = ½kBT + ½kBT + ½kBT = 3/2kBT
Rotation: linear molecules
can only rotate around the x, y axes Mean rotational energy = <εR> = ½kBT + ½kBT = kBT</εR>
why do linear molecules only rotate in x y axis?
because rotation around the z axis doesn’t move the nuclei positions.
Vibration:
Vibration: Molecules can vibrate in multiple ways depending on their bonds.
Mean vibrational energy (at high T) = kBT (per mode)
CV,m = NA × 3/2kB
= 3/2R
