## Monday, January 1, 2018

### The Laws of Thermodynamics PART 2

First Law Of Thermodynamics

This law states that the total energy of an isolated system is constant. This energy is generally the sum of its kinetic, potential and chemical energies. In some systems, nuclear, magnetic potential or electrical energy can be considered as well. While the Zeroth Law defines the temperature of a system, this law defines the energy of the system. It also states that energy cannot be created nor destroyed. It can only transformed from one form to another. The idea is the same as the broader conservation of energy law in physics, except that here we focus on internal energy. Although not a new idea in the mid 1800's, this law took time to hammer out empirically as a mathematical statement, which can be written as ΔU = Q  + W. Yet another way to express this law is dU = -PdV. "d" is used because this formula for change is written as a differential to describe a changing system. The change in internal energy of a system, in this case, is equal to the inverse of the pressure times the change in volume. There is no heat term. Sometimes, the internal energy of a system can change without any heat exchange. I mentioned a phase change as an example earlier. This can also happen when work is done at such a slow pace that heat dissipation in the form of friction approaches zero or when the system is adiabatic in nature (I will describe this kind of system in a bit).  However it is written, the first law links internal energy, heat and work. More specifically, a change in internal energy can be achieved by countless different combinations of heat and/or work added or removed from a system.

Even though caloric was incorrectly thought to be a substance bearing heat the now-obsolete caloric theory worked seamlessly with the current laws of conservation of energy and matter. It worked because it was assumed that caloric could never be created or destroyed in an isolated system. Thought of as a weightless self-repelling gas, caloric could pass through the pores in a liquid or solid from hotter areas into cooler areas. The coffee in our example cools, this theory would argue, because caloric suffused from the coffee into the surrounding air, warming it. We now know that the coffee cools because heat is transferred from the coffee to the countertop and the air through the processes of thermal conduction and thermal (infrared on our case) radiation respectively.

According to the first law, the internal energy of a system will decrease if it loses heat through thermal conduction, radiation or convection, or if it does work. The energy lost is transferred into the system's surroundings. As mentioned earlier, the total energy of the larger isolated system does not change. The internal energy of the coffee decreases as it cools but the internal energy of the room in which the coffee sits doesn?t change IF it is perfectly sealed off from any energy or material transfer, which nothing ever is in reality. In contrast, any work or heat that goes into a system increases its energy. For example, if we wind up an old-fashioned mechanical watch, we are applying potential mechanical energy to its spring mechanism. It will begin to tick and it will eventually wind down to a stop, when the potential spring energy is depleted. The energy hasn't disappeared, however. It was transferred into work ? the movements of the gears inside the watch and of the arms around the face. Some energy was transferred into sound energy as the ticking you hear. Energy was also transformed into internal friction in the spring and of the tiny gears against one another. The watch is a closed system. No matter is transferred, but heat from friction, though an immeasurably small amount, escapes the watch system into the surroundings. If we wind it up again, we have restored the system's energy by doing work on the system. The source of energy in the watch (which comes from our muscles winding it up) is transferred into work and waste heat each time. No real system has an infinite source of energy. Even the orbits of planets, etc., which seem to be eternal, are part of a system that loses energy through solar wind, resistance to the particles that make up interstellar space, and as gravitational and thermal radiation from the solar system. There is no such thing as perpetual motion. Both the first and second (as we will see) laws of thermodynamics forbid it. Even recently observed time crystals do not violate thermodynamics. These crystals spontaneously change from moment to moment. We will explore this fascinating new state of matter later on.

Thermodynamics got its start with the study of a water vapour under pressure and heat. The behaviour of fluids (gases, liquids and plasma) under pressure and heat is still one of the main focuses in this field of science. Think of air and gasoline confined in the piston of an engine cylinder. If the pressure is kept constant in this system (the piston can easily move), the work done when heat is applied to it is equivalent to an increase in volume. After ignition of the gas/air, the piston is explosively pushed up. Heat is applied and the system does work. This is called an isobaric system. If temperature is kept constant instead, it is called an isothermal system. This time, the piston is bathed in constant-temperature reservoir such as a large water bath that absorbs and dissipates heat. The piston is pushed down to compress the air. Work is done to the system and its potential energy increases. Again, pressure and volume are directly and inversely related to one another. A third kind of process, called an adiabatic process, occurs when no heat is added to or removed from the system. It differs from the isothermal process just described because in that case heat was removed from the system into the water bath. Because no heat leaves or enters the system, the change in energy depends only on work that is either done to the system or done by the system. Often, an adiabatic process is one that is too rapid for any heat exchange to take place. An example is a carbon dioxide fire extinguisher. The gas is under pressure so when it is triggered, it expands very quickly. The compressed gas is at room temperature in the canister but when it expands its becomes cold. The same amount of thermal energy is spread over a much larger volume because it is conserved. The expanded gas stays cold at first because it doesn't have a chance to exchange heat from the room-temperature air around it. No heat is added to or removed from the system. Work is done through the expansion of the carbon dioxide. It might seem confusing that the expansion of the gas in this case has nothing to do with heating it. That phenomenon is thermal expansion, in which a substance experiences outward pressure as it is heated, and it is caused by the increasing kinetic energy of its molecules exerting outward pressure.

Heat of Fusion and Heat of Vapourization

Another example of an adiabatic process is our typical winter weather here in Alberta. Warm Pacific air streaming from the southwestern coast of British Columbia hits the Rocky Mountains and is forced up the mountainside, which means a climb from sea level to about 4000 metres. For every 1000 metres the air climbs, its temperature drops almost 10°C. Air that starts out at +10°C in Vancouver (at sea level) can drop to a face-numbing -30°C at the top of Mount Robson. Then the cold air slides down the Alberta side of the mountains and this time it warms up at the same rate. By the time it flows past the town of Cochrane in the foothills (about 1000 m altitude), for example, it has warmed up a balmy (for us!) 0°C. The air cools in the mountain pass because it has moved into a lower-pressure zone so it expands (to an average of about 0.60 atmosphere (atm) pressure compared to 1 atm at sea level). No heat actually leaves the air system. The expansion itself (work done by the system) lowers the temperature, because the same amount of thermal energy is spread over a larger volume. The thermal energy is conserved, obeying the first law of thermodynamics. As the air comes down the leeward side of the mountains, it is compressed once again to about 0.87 atm at Cochrane's altitude, which warms it to about 0°C.

This is not quite the famous Chinook, however. Often, the air from the Pacific is laden with moisture, especially in winter. As it makes its way to the Rocky Mountains and it begins to climb, the moisture in the air, as liquid water, cools along with the air itself and eventually it reaches its freezing point and starts to switch over to (usually heavy) snow. When a substance freezes into a solid, it releases stored potential energy as a heat transfer. This is called either latent heat or enthalpy of fusion (the technical words for melting/freezing). The solid phase of a substance has a lower internal energy than the liquid phase because the inter-molecular bonds are stronger, providing more order. This means that the solid phase has lower potential energy. It is called latent heat because the heat lost from the substance as it freezes can't be measured as a change in temperature in the substance. A transfer of heat doesn't always coincide with a change in temperature. Latent heat is often referenced to a unit of mass. In this case it is called specific heat of fusion. The release of potential energy (as thermal energy) into the mountain air means that the air cools at a slower rate when it expands. Instead of cooling at a rate of 10°C per 1000 m, for example, it cools at a rate of about 8°C/1000 m. At the mountain peak, the temperature will be about -22°C (rather than -30°C) and about 8°C (rather than 0°C) when it reaches Cochrane, a typical Chinook day.

What exactly is happening at the molecular level? When water freezes (a phase change), the molecules "lock" into place. They lose some freedom of movement compared to liquid water, which can flow. The solidified ice has less potential energy than liquid water so it must release that energy into the system, as a transfer of heat. Water releases about 6 kJ of energy per mole (called molar heat of fusion in this case) as it freezes into ice (or snow). For this reason, snowy days tend to be warmer than clear ones. The change from steam into liquid water represents an even larger release of energy. Water releases about 41 kJ/mol as it condenses from steam into liquid, an indication of how much more potential energy the gaseous state has over the liquid state. To vapourize, water needs to absorb 41 kJ/mol from its surroundings, one reason why a warm dry breezy day is perfect to put laundry out on the line. The moist clothes have a constant supply of warm dry air to evaporate their moisture into as the water absorbs energy.

Each substance has specific values for its heat of fusion and its heat of vapourization, which depend on its unique inter-molecular bonding. In other words, each substance has its own specific latent heat. These values, in turn, contribute to the unique melting and boiling points of each substance. Specific latent heat is the amount of energy required to cause a phase change in a specific amount of a substance. If you would like to explore phase change more deeply, try my previous article "Plasma: The Fourth State of Matter." In it, I concentrate on the plasma state but in dong so I also explore what a phase change means in depth.

When a substance freezes or condenses, it releases heat into its surroundings. When a process releases heat, it is called an exothermic process. The reverse processes - melting and evaporating - require heat to move forward. They absorb heat from the surroundings, and are called endothermic processes. Water evaporating off clothes is an endothermic process.

This subject reminds us once again of the important but subtle distinction between temperature and internal energy. Temperature, explored earlier in this article, is the average kinetic energy of the molecules in a system. Internal energy, however, is the total energy of that system. It includes the potential energies of the molecules, in addition to their kinetic energies. Water vapour (at just over 100°C), for example, has more internal energy than liquid water (at 20°C) for two reasons. First, its molecules have more kinetic energy, which means it has more thermal energy (this can be measured as temperature). Second, its random molecular arrangement has much more potential energy than the more orderly arrangement of molecules in the liquid state (this can't be measured directly).

A related term is specific heat capacity. Again using water as an example, a certain amount of thermal energy must be added to a volume of water in order to raise its temperature. Specifically, it takes 4200 J of energy to raise the temperature of 1 kg of water by 1°C. Every substance has its own specific heat capacity (SHC). The SHC of steel, by comparison, is 490 J/kg/°C. What does this mean? Water can hold a lot more heat than an equivalent amount of steel can. It also requires a lot more energy to warm up than the same mass of steel does. Water, in fact, has an unusually high SHC. That is why a warm water bottle makes such an excellent foot warmer in a cold bed. A steel disk of the same mass warmed to the same temperature would not only stub your toes. It would have roughly only a tenth of the heat available to warm them up. See this Engineering Toolbox table to compare the SHC values of some other everyday substances.

Next we will explore the often misunderstood second law of thermodynamics and its implications in "The Laws Of Thermodynamics PART 3" click here.