The age of the earth and where I have been

Dear Reader,

I suspect that some of my regular readers have noticed that I have not been blogging for a while. The reason why I have stopped blogging for a while is that I am in the process of writing a book. I saw something on UK TV today which is an outrage, it is the idea that the earth is only about 6000 years old.

Now while freedom of thought and speech allows people to hold and express what ever ideas they have, even the outlandish and odd ones ! But the idea that the earth is only 6000 years old is deeply disturbing and clearly wrong !

I heard one of the young earth creationists being told by a geoscientist about radioactive dating of rocks and minerals. The creationist said something to the effect of “how do you know when the clock was zeroed”. I know that in Africa many years ago a natural nuclear reactor operated. Some of the fission products such as Tc-99 have decayed away. This suggests that far more than 6000 years has passed since the reactors were in operation.

I will leave it up to my readers to look up the half life for Tc-99 and work out how long it will take for 90 % of the Tc-99 to decay to Ru-99. Think of it as homework.

Send Assange to the land of Volvos and meatballs !

Dear Reader,

I has come to my attention that Mr Assange has just made a statement in London, I am waiting for a chance to see the text of speech.

I would like to point out that Mr Assange (and his wikileaks) is trying to campaign for everything to be dealt with in an open and transparent manner. While the legal process regarding sexual crime is quite rightly not conducted in a totally open manner (The name of the victims are never released into the public domain).

I would say that in the interests of openness and transparency that Mr Assange face his accusers in a real court and interview room rather than in the court of public opinion. I have been advised by my legal advisor that in Sweden the law is such that some interviews must occur in Sweden.

I have been told that a person who is accused of a crime in Sweden needs to attend a meeting with the police and other officials from the state. This meeting is similar in some ways to when a person appears in a UK magistrates court, while I think it is possible for a magistrate to hold a court meeting in a place in the UK such as a hospital ward it is very rare for such a thing to happen. Also I do not think it would be reasonable or legal for a UK magistrate to go to Sweden to interview a person there, in the same way it is not reasonable for the Swedish legal system to try to do something similar in the UK.

I think it would be best for all if Mr Assange was to come to the land of meatballs and Volvos to face the legal system here. If he did not force himself on the two women then.

1. He will get acquitted

2. If he gets the unfair trial he so fears or is packed off to the US, he will score a massive public relations and moral goal against the “USA” which he so fears and wants to show to be so unfair. (I think that Mr Assange not the Swedes or the US are in the wrong)

I hold the view that if he appears in a Swedish court he will get fair and reasonable treatment. If they find him guilty then he will be sent away to a holiday camp (Swedish prison) for some years. If he is acquitted then he will have plenty to write and talk about.

Greenpeace

Dear Reader,

Events over the years have suggested to me that like the curate’s egg that Greenpeace is good in parts but in other parts not so good. I hold the view that their work to protect marine mammals (Whales and Dolphins) has been a good thing, while I think their campaigns on energy, GMOs and chemicals has not been so good,

I saw with interest a blog post in which they were commenting on something which was published in Nuclear Engineering, now I would like to make a few observations.

1. The words of Steve Kidd are understood by me to be making a reference to the problem of a government trying to favour a domestic company over a foreign company. I know many governments want to avoid imports to try to protect their own industry but this is a different problem to the question of “should a country regulate industrial activity for health, safety and environmental reasons”.

I say that a country’s government has a moral duty to regulate industrial activity to make sure that health, safety and environmental standards are kept high. Maybe Justin McKeating needs to write with more care to avoid mixing up different ideas. I suspect that if I was to mix up the Rainbow Warrier with the Exxon Valdez that Justin and the rest of the Greenpeace people would be upset, I could reply that “both are ships, so what is the difference ?” but I think that this would be a lame excuse. But do not worry I know the difference between the two ships and I promise not to mix the two up.

2. The blog ends with the words “Nuclear power is an old technology – its fundamental principles have hardly evolved since the 1950s. It looks like much the same could be said for some of its supporter’s views about nuclear power’s potential “customers”.“

I would like to point out that just because something’s fundamental principles have not changed in fifty years is not a reason to view it as bad. I think that this text is the product of some very odd thinking, I suspect it may be that the Greenpeace’s blogger has made up its mind as to what the answer will be and is now whatever he/she can to get the answer wanted.

The Greenpeace blogger is trying to make the nuclear sector look bad, as freedom of expression exists the person is free to communicate their antinuclear thoughts. But I do take objection at the use of such weak logic to support the persons point of view. I think that the use of poor arguments and bad evidence by the “greens” will harm nature and the environment in the long run.

I would like to point out something, Greenpeace praises wind power but windmills (they work using the same principles as a modern wind turbine) have been around for at least 2000 years. Also many Greenpeace activities involve their fleet of ships, a man named Archimedes worked out many of the principles of  buoyancy, Archimedes did his work about 2000 years ago. So if a device is bad becuase it is based on theroy which has changed little in 50 years, then a device based on a theroy which has changed little in 2000 years is worse.

I think that the fact that a thing is based on a well understood set of principles is a good thing, it will reduce the number of nasty surpises which are possible.

If any Greenpeace supporters or staff read thing and do not like something I have read, feel free to write into me via a comment and we can discuss it like adults.

Heat capacity of gases again

Dear reader,

When I was teaching about the heat capacity of gases I went through the ways in which a gas can store energy. Now we will consider the gas to be an ideal gas, which is a series of hard spheres which have next to no volume, who do not interact with each other (unless they hit each other) which wizz around in a box. The gas molecules can bounce off the walls of the container thus exerting a force.

These moving gas molecules can move in three different dimensions thus we need to consider the kinetic energy stored in the movements in three different directions at 90 degrees to each other

If we consider nitrogen gas, then the mass of each molecule will be 28 atomic mass units, so one mole will have a mass of 28 grams.

Now at constant volume the heat capacity of a diatomic ideal gas is ⁵/₂R, the reason it is higher than the ³/₂R for a monoatomic gas (like argon) is that the molecule can spin and thus store energy spinning on the x axis, and the y axis. As it is linear it can spin all it likes on the z axis but it will never store any energy by doing so !

Energy of a rotating object = E = ½ Iw²

As the value for I for rotation on the z axis is zero, you should be able to see that on one axis the molecule is never going to be able to store any energy.

For rotational energy of a diatomic molecule

E = B J(J+1)

J is the number of the spinning state (it can only be an integer), while B is a constant for the molecule. If we take B as being given by.

B = h / (8 pi² c I)

Lets do some dimensional analysis on this

As for a diatomic molecule, I = [(m₁m₂)/(m₁+m₂)]r²

Where r is the bond length, then the units of I will be kg m²

Thus the units for B will be Js / (m s^-1 kg m²) = N m s / (m s^-1 kg m²) = N s² kg^-1 m^-2

This looks like a bit of a mess, then we read it a second time and see that it says under that equation (on the wavenumber scale). So it is clear we have the wrong equation.

At a university physics site it gives a different expression for B

B = h² / (2 x 4 pi² x I)

If we do the dimensional analysis for this then we get

J² s² / kg m² = N² m² s² / kg m² = N² s² / kg = N m s^-2 s² = N m = J

Much nicer !

Then the moment of inertia for the nitrogen molecule will be given by

{(2.32481 x 10^-26 kg x 2.32481 x 10^-26 kg) / (2.32481 x 10^-26 kg + 2.32481 x 10^-26 kg)} x (1.1 x 10^-10 m)² = 1.41 x 10^-46 kg m²

So as planks constant (h) is equal to 6.62606957 x 10^-34 J s, we can calculate B

B = (6.62606957 x 10^-34 J s)² / (8 x pi² x 1.41 x 10^-46 kg m²)

B = 3.95 x 10^-23 J

Now if J changes from 0 to 1 we will need 2B of energy

This will be  7.9 x 10^-23 J

The frequency for this photon energy is 1.19 x 10¹¹ Hz (119 GHz)

This puts these photons in the upper end of the microwave spectrum, the highest frequency I am currently licensed for is 250 GHz but I do not know if anyone has managed to build equipment for this frequency. I suspect that this frequency allocation is something which is there for the future.

But back to our problem of nitrogen, based on the energy of the photons and the number of molecules in a mole, we can say that one mole of 119 GHz photons will have an energy of 47.6 joules.

This corresponds to about 4 cm^-1 radiation.

As C_v for argon is equal to ³/₂ R = 8.3144621 J K^-1 mol^-1 x 2/3 = 12.47169315 J K^-1 mol^-1 then it is very clear that at room temperature gas molecules will have the energy required for them to start to spin.

At room temperature a mole of an ideal monoatomic gas has 3717 joules of internal energy.

On the other hand if we consider a typical vibrational frequency for a triple bonded diatomic then it will be about 2200 cm^-1.

A mole of an ideal diatomic gas will have at room temperature will have 6194 joules of energy, the inverse wavelength (wavenumber) for the nitrogen corresponds to 66000 GHz (66 THz) which means that one mole of these photons will have an energy of 26335 joules.

Thus as a typical molecule only has about 25 % of the energy required to start to store energy by vibrating, as a result very few nitrogen molecules will be able to get more than the zero point energy for their vibrations.

Thus we only consider the translational energy and the rotational energy of a typical diatomic gas when we try to work out Cv and Cp.

Example of a DSC trace

Dear Reader,

For those of you who want to see what a DSC trace looks like here is one.

DSC trace for substance X

For legal reasons I would rather not say what the substance is in the machine, but you should be able to see two endotherms. One is at 90 °C and the other at 130 °C. Sadly the base line is not quite perfect, while in the text books you tend to see perfect looking spectra in real life often things are not quite perfect looking in any spectroscopic method.

Thermodynamics

Dear Reader,

As my friend and fellow teacher is away in Germany I had to teach thermodynamics to the first years. I have to admit that I do not love all aspects of classical thermodynamics which is a bit of a misnomer it should be thermostatics as it deals mainly with static states.

One of the things I do not love about thermodynamics is that classical thermodynamics tells us nothing about how fast or the mechanism by which we go from A to B. All it tells us is the difference between A and B. The more modern thermodynamics which is based on the molecular motion can tell us more but I think that I will leave that some either some other day or some other person to write about.

As an incurable organic / inorganic chemist I love mechanism, mechanism explains to us how things happen. From that we can know what can and what can not happen.

One of the questions which I had to teach was the idea that we take an ideal gas and consider the heat capacity both under constant volume and constant pressure conditions.

For a monoatomic gas such as helium the heat capacities are

Cv = R 3/2 (constant volume)

Cp = R 5/2 (constant pressure)

If we were to assume that we have 2 grams of helium in a box which has a fixed volume of 1 litre then the box will have a pressure. The temperature of our box is 273 K. The formula mass (FW) of helium is 4 g mol^-1

We can calculate this with PV = nRT

If we assume that R is equal to 8.3 J K^-1 mol^-1 then we can calculate P

n = M / FW = 0.5 moles

P = nRT / V = 0.5 mol x 8.3 J K^-1 mol^-1 x 273 K / 1 x 10^-3 m³ = 1132950 Pa

OK so we have a start pressure of 1132950 Pa, or for those of us who do not like so many points before the decimal point we have about 1133 kPa or circa 1.133 MPa. This is about 10 bar.

Now if we heat the box up to 100 ^oC (373 K) then the energy of the helium will increase.

As Cv = ΔU / ΔT

We can rearrange our equation to give us

Cv ΔT = ΔU = 8.3 x 3/2 x 100 K = 1245 J mol^-1

As we have half a mole then we have to put in 622.5 J of energy if the volume is going to stay the same. The pressure will increase we can predict it with the following equation.

P₂ / P₁ = T₂ / T₁

My calculations give us a value of 1547950 Pa for the final value.

Now lets do it again with constant pressure

As Cp = ΔH / ΔT = 5/2 R

If the pressure stays the same then the amount of energy required will be higher at 1037.5 J.

We might for a moment ask why is the energy higher for the fixed pressure case than it is for the fixed volume.

When the gas is heated up at a fixed pressure then it has to expand to continue to satisfy the equation PV = nRT

We can calculate the volume increase

V₂/V₁ = T₂/T₁

So the box has to increase by 366.3 ml to a volume of 1.3663 litres or 1.3663 x 10^-3 m³

Now E = P ΔV

For fun lets do the dimensional analysis

Joules = N m^-2 x m³ = N m

Now E = P ΔV = 1132950 Pa x 0.3663 x 10^-3 m³ = 415 J

Now 622.5 J + 415 J = 1037.5 J

I am hoping that you can see that the difference between the two energies which need to be added to the gas to increase the temperature. I hope to add some diagrams shortly.

Cesium chemistry in Japanese soils

Dear Reader,

After having spent much of sunday in a fruitless search for a storage box for my garden tools, I get the chance to write to my beloved readers another blog entry. Now all along I had been making the prediction that the cesium would stick like glue to the soil and stay in the top layer. Some workers have examined soil samples and in a paper (Takeshi Fujiwara, Takumi Saito, Yusa Muroya, Hiroyuki Sawahata, Yuji Yamashita, Shinya Nagasaki, Koji Okamoto, Hiroyuki Takahashi, Mitsuru Uesaka, Yosuke Katsumura and Satoru Tanaka, Journal of Environmental Radioactivity, 2012, 113, 37-44) an examination of soil samples from the Fukushima area has been reported. In this paper it has been shown that the cesium is concentrated in the top layer of the soil.

Circa 70 % of the cesium is in the top 2 cm in the soil, while the iodine was more mobile. The good news is that the cesium will not enter ground water, further good news is that plants with deep root systems are unlikely to absorb much cesium. The bad news is that the cesium will be in the right part of the soil to enter grass via its shallow roots and the fact that the cesium is in the upper layers of the soil will increase the external threat due to gamma photons.

It is interesting to note that the Japanese may not worked out a sensible way to store the contaminated soil which is removed during the clean up of land. It has been reported that people are being required to store contaminated soil from cleaning up their own gardens on their own land. I think it would be better if industrial estates were used as places to store the contaminated soil while the government find a place to store the soil for the next 300 years.

I have spoken to my legal advisor about human rights, and my advisor told me that the right to have a safe environment could override the right to object to a waste store in a given town. I hold the view that if the waste stores are sited well away from homes and other places where the general public spend a lot of time, then it is OK to raise the dose rate in the waste store. The waste store should be designed to avoid releasing cesium into the environment and the construction of the waste store should be done in such a way that it does not increase the dose rate at the edge of the site. I think that the reference dose rate for the latter point should be the dose rate at the edge of the site before the clean up is done.

If the dose rate at the edge of the site is 2 microSv per hour, then this will give a person a dose per year of 17.5 mSv which is a big dose for the general public. But if the dose rate at the same spot was 2 microSv per hour before the clean up which generated the waste which will go into the store is conducted then the clean up will have a neutral effect at the edge of the waste store but will have a good effect on the majority of the land.

I may do some calculations on the subject if I get time in the near future.