You All Meet In An Inn

There is a tendency in certain mindsets to dismiss a certain popular wiki known as TVTropes as an over-analytical media dissecting machine, and while I think there is truth in that argument, there is also truth in the idea that Tropes Are Not Bad, and I would like to take a moment to justify one of the more well known tropes in RPGs.

So you start your game, all your characters are ready, and the GM has donned whatever piece of clothing makes himself feel that touch more important (I have a particularly nice top hat). You are awaiting the GM's first words eagerly/absently doodling on your character sheet when you hear the words: "You are all sitting in a pub/bar/space bar in space". Instantly the table erupts in groans and accusations of a severe lack of originality are thrown around. But why? The way I look at it, your GM has chosen one of the most likely places for a group of people to meet up. If they know each other, what better place to hatch your plans that in your favourite local? If you have all just met, how better to loosen up than with a round of drinks/futuristic hallucinogenics.

You all meet around an array of novelty shots.

I will grant that in the everyone-knows-each-other setting maybe someone trusted's home would suffice, though in all likelihood, someone will still call out for the host to provide at least a glass of water, in startling resemblance of the RL group itself. But the usual setup in the cliché is that a group of people bound by common cause meet from afar at an inn, a well known landmark in any town. Your character who is not from town can easily ask a passing stranger "Where is The Juggling Tomcat?" and get a positive answer. There is however little chance in all but the smallest towns of getting where you need to quickly with a "Where is Urist McHammerdorf's home?"

My final point lies in the often all too looked over effort required of the GM to come up with somewhere for a bunch of characters who really have no business being together to meet. This ties back to the previous points that really, the best place for an upbeat sniper specialist and a depressive technomancer with Occult (Herbalism) to meet up is somewhere neutral, somewhere both can easily locate and no-one feels overly uncomfortable.

"Do you reckon they know any Michael Buble?"

In summary, there is nothing particularly wrong with the trope. If your GM pulls it out, and you really have a problem with it, just consider it an unoriginal starting point for an adventure that you can make brilliantly original yourself. And GMs, if you are really stuck for a logical starting point for your diverse set of characters, you can do worse than an inn.

If nothing else your PCs can start a bar brawl. That should keep them entertained while you figure out which crime lord they pissed off doing so..


NB: You'll thank me, dear Reader, for not actually linking you to any TVTropes pages. It would have resulted in hours of lost productivity for both of us, I'm sure.

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Thermal Physics: Ideal Gas Equation and Laws

pV = nRT

That equation is gorram everything to this section.

Learn it. Love it.

Wear it into town.

Pressure, p
This is caused by the gas particles colliding with the wall of whatever container they're in. Measured in pascals, Pa

Volume, V
The space occupied by the gas. Measured in m³

Number of moles of gas, n
That's fairly self explanatory, really. Measured in numbers.

Molar gas constant, R
= 8.31 J mol^-1K^-1

Temperature, T
The measure of the average kinetic energy of the molecules of a gas. It is the absolute temperature and is measured in kelvin, K


Now, a little something about temperature scales. The temperature of gas is measured by the change in another substance at the same temperature. The obvious example of this is a glass thermometer, and the expansion of a length of mercury or alcohol within. This is known as a thermometric property.

The thermometric property is measured at two fixed points. Often this is at the change of state of a property. It is well known for example, that the Celsius temperature scale was made to be fixed at 0 °C and 100 °C, the then defined freezing and boiling point of water. So let's come back to our glass thermometers. They are designed so at 0 and 100 they are both accurate. It is assumed therefore that the two will progress linearly up and down the scale. Alas as is so often the way, things are a little more complicated.

Mercury and alcohol expand at different rates as they heat. The consequence of this is that while they both agree at 0 and 100 °C, these are the only points they can be guaranteed to agree on. But fear not. It was to overcome this that a standard scale was devised. May I thus reintroduce: Kelvin.

William Thomson, 1st Baron Kelvin OM, GCVO, PC, PRS, PRSE

The Kelvin scale is actually based on our post subject, the behaviour of an ideal gas. It uses the pressure of an ideal gas as it's thermometric property, it's two fixed points being the point at which there is 0 pressure, known as absolute zero and the triple point of water, where water can exist as solid, liquid and gas, defined to be 273.16 degrees on the Kelvin scale.

Gas laws

Remember that equation I ordered you to remember? These 3 are what combine captain planet style to form it.

  1. Boyle's Law

For a fixed mass of an ideal gas at constant temperature p ∝ ¹⁄_V
∴ pV = constant  or p₁V₁ = p₂V₂

 2. Charles' Law

The volume of a fixed mass of an ideal gas at constant temperature is proportional to it's absolute temperature, V  ∝ T

 3. The pressure-temperature law

The pressure of a fixed mass of an ideal gas at constant volume is proportional to it's absolute temperature,  P  ∝ T.

Now, you do need to know these. At the very least, you need to associate the name with the key components, because then you can just look at the equation up top to work out what they're meant to be doing.

More constants!

The Avogadro constant

The corresponding law states that at the same temperature and pressure, equal volumes of gases contain equal numbers of molecules.  Lot of words, sure, but it's not that bad at all. Let's refer back to our beloved equation. Rearranging for number of moles give us:

n = ^pV⁄_RT

It is clearly apparent that if p, V and T are the same for two gases then yes, they will have the same number of moles.

We take this a step further by considering 12g of Carbon-12. It has as many atoms as there are particles in one mole of a substance. This gives us the Avogadro constant, N_A = 6.02 x 10²³

The Boltzmann constant

This is literally just a constant gained by taking our two current constants and dividing them:

k = ^R⁄_NA

k = 1.38 x 10^-23 JK^-1

• Back to Heat Capacity and it's related paraphernalia.
• Onwards, to kinetic theory!

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Thermal Physics: Heat Capacity

In Britain's own peculiar way it is bloody freezing, in the middle of June. So, what better time than now to do a little something on thermal physics.

As with most physics, this all comes down to energy, and the transfer, exchange and general movement of same. The effect of this is generally kind of obvious. The more thermal energy something has, the larger it's temperature is. What's interesting is that various materials have a greater inclination to be heated that others. This is easier demonstrated. Find a metal surface, and consider it's temperature. Unless you already know what I'm about to get at and are purposefully being difficult by considering the inside of an oven, you should agree that said metal is at room temperature. Now if you touch said metal, you should notice that it is quite cold. "Gosh James, how can this be?" I hear you ask. Well, as we all know, heat tends to flow to colder areas. Things like to reach an equilibrium, that's just they way of things. So when you touch metal, you aren't feeling cold metal as much as you are feeling the heat energy in your fingers being SUCKED OUT FROM YOUR BODY.

Dramatic reconstruction

The way we measure how willing objects are to drain the life from your very body is called the specific heat capacity, c. This is defined as the energy required to cause a temperature rise of 1K per unit mass, usually 1 kg. From it we can work out a bunch of stuff with the equation:

ΔQ = mcΔT

In words, the change in thermal energy of an object is equal to the mass by the SHC by the change in temperature. T is measured in kelvins really but given that 1 K and 1 °C is exactly the same it doesn't really matter once you stick that Δ there.

All important equations are given to you but I feel it's helpful to get to know them beforehand. So let me throw this one at you:

 ΔQ = ml

This is where we bring in latent heat, l. Again this comes with a "specific" alternative. Two actually, and as such we have two definitions to remember. Both are pretty similar however, so I don't imagine you will have too much trouble.
Specific latent heat of fusion

the energy required to chance 1 kg of solid into 1kg of liquid, with no change in temperature.

Specific latent heat of vaporisation

the energy required to change 1 kg of liquid into 1 kg of gas with no change in temperature.

What this means for you is that when working out the energy required to  get a substance from one temperature to another, and there is a state change in between, you are going to need to make more than one calculation. One for the first temperature increase, one for the state change, then another for any further temperature increase. Keep yourself aware of this and you should be fine.

On the practicality side of things, this area of physics is widely used, mainly in the area of cooling, by dissipating thermal energy. It can been seen in power stations, and closer to home, us when we sweat.

Continue into the world of ideal gases

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Bailyn's Fables: Chandrasekhar's Limit

First, we need to know a little something about white dwarfs and electron degeneracy pressure. You see, the normal way stars manage to not collapse into their incomprehensibly massive selves is thermal pressure. Basically, while gravity is pulling everything in, pressure is pushing everything back out, and so the two balance, at least, for a while. Eventually the star runs out of hydrogen in the core, which contracts, raising temperature of a shell of hydrogen outside the core, causing it to start fusing. This expands the star into a red giant, until all remaining hydrogen has been fused, making the star contract again.

What it doesn't do is collapse into a black hole. It seems that for high density objects other kinds of pressure arise. In this case it is electron-degeneracy pressure. Very, VERY basically, this is a result of no two particles being able to occupy the same space, and the pressure that results as the volume these particles are occupying decreases. Long story short is that this pressure fights against the gravity of the collapsing star, balancing at roughly the radius of the earth. This is called a white dwarf, and this is where we pick up the main subject of this post.

In the 1930s an Indian-American called Subrahmanyan Chandrasekhar discovered that electron-degeneracy pressure isn't always enough. If the mass of the star is more than 1.44 solar masses gravity overcomes the pressure and the star continues to collapse. He presented his findings to the Royal Astronomical Society. Upon finishing however Sir Arthur Eddington stood up and opposed Chadrasekhar's findings, stating:

 I think there should be a law of Nature to prevent a star from behaving in this absurd way!

A full account can be found in , pages 37-39. It is apparent that while he could understand the theoretical idea of a black hole, Eddington simply could not conceive of Chadrasekhar's findings, that beyond a certain mass a star could essentially collapse into nothing.The result of this was that a number of physicists who would otherwise have publicly agreed with Chadrasekhar did not, due to Eddington's status. Chandrasekhar spent the rest of his life holding to his beliefs, even until 50 years later when he finally got the Nobel Prize for his work.

The moral of this tale is that maybe one should believe their student, rather than their own intuition. Had Eddington allowed for Chandrasekhar's work to be possible, we might not have lost a good 40 odd years of research into black holes. It also demonstrates the dangers of being too convinced of one's own intellect. As Eddington got older he became more and more convinced that he could just guess the answer to questions using gut instinct, a method I imagine most of us would agree to be utterly useless scientifically.

Further reading

A review of the meeting in which Chandra presents his findings and Eddington tears them down. Relevent pages are 37-39
The highlights of Chandra's life
A brief biography, and image source for this post

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Transit of Venus 2012

Early this morning I became part of history, and witnessed the like of which will not be seen again for over a century. I saw the transit of Venus.

I thought I'd break my unintentional hiatus just to express to the aether just how I felt at such a prospect, not to mention witnessing the historic event itself. I switched on the NASA EDGE livestream at 20:45 GMT, and watched for the entire stream from then until 06:00 the next morning. For most of the night I had been resigned to the fact that all the weather sources had said just how cloudy it was going to be, so I contented myself with the stream, which was incredibly informative and entertaining, I must say. However, as 04:00 approached and the sky became lighter, I noticed that the cloud was breaking.

Then came a good hour and a half of fervent hope, that the sun might breach the horizon before the dark mass of cloud to the north reached us. I happened to have a decent pair of welding goggles ready (bolstered with a pair of sunglasses, just in case) and sure enough, for a few minutes at around 05:45, just before 3rd contact, direct sunlight broke through the clouds, and after a few seconds, I could make out a speck of black at the edge.

I was struck by how beautiful the whole thing was. It really pulled into view the idea of the Earth and it's place in the Keplerian dance that is our Solar System, and our fiery sister planet, so alike but so different to Earth.

It was cloudy over most of Britain, so I imagine that yes, a significant number of people in this country did not get to see what I did, and may who could likely didn't care. But that's not really the point. I didn't so much become part of a select few, as I did join so very many people in celebrating this event. Not only the millions watching the same stream I did, or the other streams across the world, but the further so very many who have witnessed the same event over millenia. This event connects us to the past and the future, and that in itself is incredibly humbling.

The Science

Of course it is a great deal more than just a stunning celestial event. The transit has provided much for scientists, significantly in the area of studying exoplanets, one key method of discovering such is looking for the periodic dips in light from other stars that mean something is passing in front of it. As the sun is reaching a maximum in it's activity cycle it has more sun spots that usual. The transit means that astronomers had a chance to practise observing similar events in other stars.

Further practise can by made into estimating exoplanet diameter, through the measurement and comparison of Venus' apparent diameter and known diameter

Observations of Venus' atmosphere can help us understand more about it, more than can be cleaned from normal observation. It can also be compared to exoplanets to help determining atmospheres yet unknown.

All in all this was a highly significant event for all involved, from the amateur observers, looking at the pretty colours in a filtered livestream, to those dedicated scientists who missed the event, opting instead to sleep in anticipation of the huge amount of data and work that is about to be flung their way.

Images courtesy of NASA and SDO, link below

Now if you'll excuse me, I have to go get my sleep schedule back in order.

P.S.
If you missed it, or you just want to see more, I have a few links to share:

• NASA's Transit Data, a number of short clips and composites of the event in various filters, taken by the Solar Dynamics Observatory 
• Helioviewer, an impressive tool that, in short, shows you the sun. 
• Sun-Earth Day, the NASA sub-site with a large amount of information and images on and of the transit.
• NASA Edge, The guys who provided/hosted the livestream. They were clearly effected by the lack of oxygen up at the top of Mauna Kea, and they plugged it enough themselves, so I see no harm in linking to their stuff in appreciation.
• MMS, nothing to do with the transit, but a highly interesting upcoming mission that was mentioned in an interview during the livestream.

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