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# First law thermodynamics applied.

The first law thermodynamics students learn is that energy can't appear or disappear.   The only thing it can do is change form.  In other words, you can't create or destroy energy, but you can transfer and transform it. Energy can move between a system and its surroundings, changing forms. The first law of thermodynamics can be expressed mathematically as:

ΔU = Q - W

This equation has ΔU as the change in internal energy, Q as the heat added to the system, and W as the work done. In this equation, heat or work, or both, must be added to a system when its internal energy changes. In many physical systems, this law is used to measure the energy change in a system.

Thus in a confined system, like a single room, the total energy changes when heat energy is added minus work done by the system on its surroundings (blowing out the walls, for example).

According to the first law of thermodynamics, you can calculate the change in "real" temperature.  By adding or subtracting heat, minus the energy returned by expanding or compressing the air, it would increase or decrease.

That's what meteorologists call the potential temperature.  We need a bunch of instruments that measure temperature at different pressures.  Then we can apply this first law thermodynamics.

What is this important weather instrument package? It's called a radiosonde.  Hundreds of helium-filled weather balloons go up every day around the world, so we can build a crude model of the upper atmosphere.  For weather forecasting, it's crucial.

To interpret the data, meteorologists use thermodynamic charts like skew-T log-P, tephigrams, and hodographs.  Many standards are incorporated into them, like the first law of thermodynamics.

You can also analyze data with an upper isobar weather map.  They let you compare data from multiple locations at once.

## The tephigram chart

is used by forecasters in many countries, including Canada.  The area within an isobaric box on this chart is proportional to the energy involved in a physical change.  By doing this, you can see how the first law thermodynamics works.

1. Look at the slightly curved lines going left to right.  Each one has two labels.  In the box, pressure in millibars (a millibar is one tenth of a kilopascal) and altitude in metres, technically called geopotential.
2. First law thermodynamics tephis are made up of two sets of straight lines, one sloping upward to the right, the other perpendicular to the right.

• We call those lines up to the right isotherms.  Each one represents a different temperature.  This sample chart shows one tephigram line for every 10°C, and more precise ones show one for every single degree.
• Straight lines inclining leftwards represent potential temperatures.  As we may or may not know, these so-called dry adiabats have values in Fahrenheit, Celsius, as shown here, or Kelvin, which is Celsius plus 273.  They show the path a parcel of dry air would take if it were to descend, go downhill, and undergo a pressure increase without gaining or losing any heat or moisture from the sun, the ground, or anywhere else.
• The first law of thermodynamics applies here.  See where each dry adiabat crosses the 1000 mbar pressure curve.  100 Pascals is a millibar, mbar or mb.  Isotherms crossing that intersection display the same temperature value as adiabats.  It's because we define potential temperature using 1000 mb pressure.
• See the broken curved lines?  One says saturated adiabat.  They're called pseudo-adiabatic lines by some scientists.  Near the bottom of the chart, they're almost vertical and gradually approach the angle of the dry adiabats near the top.
• Their web-bulb potential temperatures, used to label these curves, intersect the 1000 mbar curve (closest one to the bottom)
• Look at the slightly curved lines going left to right.  Each one has two labels.  In the box, pressure in millibars (a millibar is one tenth of a kilopascal) and altitude in metres, technically called geopotential.
• First law thermodynamics tephis are made up of two sets of straight lines, one sloping upward to the right, the other perpendicular to the right..
• at isotherm values.  In the example above, there are no labels for them.  Under the same conditions as the previous illustration, completely saturated air goes up the hill.

## First law thermodynamics example

There's a big difference between moist and dry air.  Look at the space between the red and blue lines at 800 mbar.  It's all latent heat from evaporation or condensation.  That's the heat moisture gives off or absorbs when it goes from vapour to liquid.

The blue one is the dry one; that's why it's called Sahara.  At sea level, around 1000 mbar, it easily reaches 30's or more (or 90's and above Fahrenheit).

A set of faint broken lines slants up to the right at a steeper angle than the isotherms if you look closely.  This chart doesn't show these lines well but those values are also important.  They're saturation mixing ratios.  The lines correspond to specific vapour contents and are labelled in grams of water vapor per kilogram.

Nomograms can be included in more elaborate diagrams.  Nomograms are tables and scales that make quick calculations, like converting dew point temperatures to frost points in cold areas.  Like an old slide rule, they make analog rule-of-thumb calculations.

Nomograms let meteorologists figure out heights and thicknesses of air packages, elevations at interpolated pressure levels, and virtual temperatures.  Humid air's virtual temperature is the temperature dry air would have to be to have the same density as humid air.  Water molecules are lighter than air, so it's usually a degree or two higher.  A higher temperature will compensate for that.

We can also plot wind data on a chart called a hodograph.  Wikipedia has more info on this one.

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## Skew T Log P diagram

This graph is a good alternative to the tephigram.  The similarities outweigh the differences, and the USA National Weather Service seems to prefer this one.

All the other curves are gentle, except for the isotherms, moisture content, and isobars.  The first law of thermodynamics and other laws don't change.

You can see the latest skew-t plots for various locations in the US and Canada.

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