Heat Flow and Work – Thermodynamic Coupling
Thermodynamics is part of physical chemistry and studies heat and work and the interrelation between measurable quantities. One of the driving forces in Nature is the flow of energy from a hotter place (the hot reservoir) to a colder place (the cold reservoir or the outdoors). In the process work can be extracted from a particular system using an engine.
Every process that takes place in the universe involves heat flow which, along with entropy flow, characterize events. Energy flows down to a minimum and entropy increases to a maximum. The changes can be small, like a protein moving a molecule in a bio-process or large, like a supernova. We all know the Force of Nature from storms and Earth quakes which cause destruction (an increase in entropy). In his drive to improve his environment, the goal of Man is to understand and harnessing those forces. To do so it is necessary to understand what happens in the most basic terms.
Eighteenth century scientists were intent in improving the efficiency of the steam engine. In order to study it, the engineering can be broken down into ideal steps. Losses due to friction, heat loss, slipping belts, etc can be ignored. After all those losses can be minimized by obvious improvements, so at the end, we can get to the heart of the thermodynamic process of extracting work from energy in the most efficient way.
Energy flows from one place to another driven by a difference in temperature. If the temperature difference is large, heat flows faster. Equilibrium is established between two systems when the temperature is the same. This is called the Zeroth Law of Thermodynamics:
The Zeroth Law of Thermodynamics says: if two separated systems are in thermal contact with a third, then at equilibrium they all have the same temperature.
Clearly when we bring two blocks together, heat will flow between them. This is an example of coupling systems A to B and to C so eventually the three will be in equilibrium. This coupling only allows heat to flow through direct contact.
Rather than just heat flowing from a hot place to a cold place, we might like that heat to be converted into work. Then we must capture some of that heat energy by a device, or some kind of engine. An engine converts energy into work.
In summary when heat flows from the hot reservoir (the heat you pay for) to the cold reservoir (the outside) some of the heat can be converted into work and some remains as heat. Since energy is a state function, then the First Law of Thermodynamics states that when energy flows between hot and cold reservoirs, some is converted into work, w, and some remains as heat, q,
The internal energy, ∆E, is a state function, but heat and work can vary depending upon the efficiency of the engine. Consider the internal energy change is a liter of gas burned in a car. There is always some heat loss, you cannot get away from that, but we want to get as much work from that liter as possible. That is efficiency. Of all the different ways (we call them paths) of extracting work w from a system (a liter of gas) one path is theoretically the most efficient. Heat and work are not state functions because they depend upon the path. Look at the following image, and pay attention to the signs and apply conservation of energy:
The system is the engine which does work on the surroundings. Notice that work is expressed with a minus sign. That is because energy, heat and work are defined relative to the system (the engine). Energy +qH goes into the engine and some goes into work, –w, done on the surroundings and some heat flows into the surroundings, -qH.