Summary of all content of the given lectures of thermodynamics for biomedical engineering & pharmacy students at the RUG. It is summarized in the order of the given lectures. All important formulas and graphs are included and explained.
Formula sheet physical organic chemistry 1 (NWI-MOL157)
Atoms, Molecules and the Periodic Table
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Biomedical Engineering
Thermodynamics (WBFA021)
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Thermodynamics 2020-2021
Lecture 1
4-1-2021
Basics of thermodynamics:
1st law of thermodynamics: Energy can neither be destroyed nor created. You cannot create energy
from ‘nothing’. Otherwise no oil or other fuel would be needed.
2nd law of thermodynamics: No process is possible in which the sole result is the absorption of heat
from a reservoir and its complete conversion into work. E.g. dropping a ball, the ball does not bounds
back as high as it started. There is loss of energy.
With thermodynamics we look at equilibria using macroscopic states, like pressure, volume, energy,
etc. It is not described on a microscopic state, like molecules. The microscopic states such as place
and rate of individual molecules are not relevant. Molecules can maybe explain some macroscopic
results, so they might still be mentioned.
Chapter 1: gases
Perfect (/ideal) and real gases differ in their properties.
Perfect gases:
- The gas consist of molecules with a mass m and a diameter d, which move randomly.
- The diameter of the molecules is negligible with respect to the distance between the
molecules.
- There are no interactions between the molecules, except for elastic collisions.
When this is the case, we can use ‘Boyle’s and Gay-Lussac’s law’.
𝑹𝑻 𝑹𝑻
p=n Vm = 𝑽/𝒏 p=
𝑽 𝑽𝒎
p = pressure (N/m2)
n = number of moles
R = gas constant (8.3144 J mol-1 K-1 → SI unit)
T = temperature (K)
V = volume (m3)
State function: the variables cannot be chosen totally independently. Variables like pressure (p),
molar volume (Vm) and temperature (T) describe the state of a gas and are so called state functions.
If you choose one variable, another one is fixed. E.g. T = … then T cannot be chosen independently
(it’s a function of p and Vm), but p and Vm can. They can variate.
A process can be path independent. Only the initial and final physical states are relevant, just like
only the starting locations and your final location
matters and not the route you take. When this is the
case → state function. The question then is, why don’t
we go directly from A→ D and take a detour? This is
because you then only change two variables instead of
three variables. The detour can be handy in this case.
During each subprocess, only two variables are
changing.
,Pressure
In a perfect gas molecules move randomly and there are no interactions between the molecule
except for elastic collisions (no dissipation of heat during collision). The collisions also happen against
the wall of the container. The frequency and intensity of collisions against the wall is called pressure.
The unit of pressure in SI-unit is both Nm-2 and Pa. They are equal to each other. Stander conditions
are 1 bar = 105 Nm-2 = 105 Pa.
p = ρHg . h . g = 13546 x 760 x 10-3 x 9.81 = 105 Pa.
(the density of mercury is 13546 kg/m3)
In a barometer the mm of mercury can be converted/equaled to the pressure. 760 mm mercury
equals 1 Bar.
The mercury replaces air, so you have to take this into account for the pressure difference.
Δp = h (ρHg – ρair) g ≈ 𝒉𝝆hgg
However, density air is negligible as compared to density mercury.
Temperature
There are two laws of thermodynamics, but they realized later that temperature should be included.
This is why they included the 0th law. It is about thermal equilibrium. It can me measured in Celsius,
Kelvin and Fahrenheit. The lowest possible temperature is -273 ˚C = 0 K → K = ˚C + 273. For
thermodynamics, when dividing temperatures always use kelvin scale. When subtracting
temperatures (ΔT) both Celsius and Kelvin scale can be used.
When there are two objects in thermal equilibrium that do not touch each other, there can still be
transport from heat. In that case it is a diathermal wall (permeable for heat). You can also have an
adiabatic wall: not permeable for heat.
Isothermal process: temperature remains constant.
Adiabatic process: temperature can change.
When heat cannot go away (adiabatic wall), the temperature will change when you heat up
something in a container for example. The temperature will go up. This happens during an adiabatic
process. When the wall is permeable for heat, diathermal wall, the heat can go away and the
temperature will remain constant.
Isochoric process: volume remains constant.
Isobaric process: pressure remains constant.
Three types of systems:
- Open system – exchange of both energy and matter is possible (e.g. when heating water, it
can dissipate out).
- Closed system – only exchange of energy is possible (amount of mass stays the same).
- Isolated system – exchange of neither energy not matter is possible (e.g. thermos bottle.
Heat remains the same and no matter can go in or out).
Outside of the systems are the surroundings. System + surroundings = ‘everything’.
What can be a system? Examples:
- A vessel containing a gas
- A vessel in which a chemical reaction occurs
- A living cell
- A human
- A steam generator
- The earth / the sun / a planet / our solar system.
𝐑𝐓
Pure gas: p=𝐧
𝐕
𝐑𝐓 𝐑𝐓 𝐑𝐓
Mixture of a and b: p = (𝐧, 𝐚 + 𝐧, 𝐛) = 𝐧, 𝐚 + 𝐧, 𝐛
𝐕 𝐕 𝐕
𝐑𝐓
Partial pressure: pa = na
𝐕
In general: p = p a + pb + …
, The number of moles can be split up in a gas mixture. With this you can calculate the partial pressure
of gas a and gas b. They both contribute to the total pressure.
Measures/ expressions of composition:
Absolute
- Molarity → number of moles per liter of solution, c.
- Molality → number of moles per kilogram of solvent, m.
Relative
- Mole fractions → number of moles per total mol, x.
- Weight fractions → weight per total weight, b.
The relative measures have no unit and will always be between 0 and 1. The absolute measure has a
unit.
The total pressure of partial pressures can also be summed up by mole fractions. Xa = na/ntotal. p = (xa
+ xb + …) p.
In a binary gas mixture, when Xa is at its maximum, so Xa=1, then Xb =0 and the other way around.
Lecture 2
5-1-2021
Chapter 1 continued
Real gases do not obey the three requirements of the perfect
gases (at least not one of them).
When the potential energy is positive, there is repulsion and
when negative, there is repulsion. When the molecules are at
great distance from each other, they behave like perfect gases.
When they are far away from each other, they are too far to
attract or repel each other. When they come closer together,
there is attraction. When they are even more close, they will
repel each other, because the diameters start to overlap.
Van der Waals forces:
- Orientation-effect. Present at gases with a permanent dipole, for example CO (C is partial
positive and O is partial negative).
- Dispersion-effect. Present at gases without a permanent dipole, for example He (one side is
partial negative and one side partial positive in
He).
In a perfect gas, there is no net attraction or repulsion
(like on the left).
The orientation of the molecules more towards the
inside of the container → attraction dominant. Pressure
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