The laws of thermodynamics are deceptively simple to state; however, they are far-reaching in their consequences. The very first law asserts that if heat is recognized as a form of energy, the total energy of a system plus its surroundings is conserved; in other words, the total energy of the universe remains constant.
The first law is put into action by considering the energy flow throughout the boundary, separating a system from its surroundings. Take into consideration the classic example of a gas enclosed in a cylindrical tube with a movable piston. The wall surfaces of the cylindrical tube act as the boundary separating the gas inside from the world outside, and the movable piston provides a mechanism for the gas to do work by expanding against the force holding the piston (assumed frictionless) in position. If the gas does work W as it expands or absorbs heat Q from its surroundings through the wall surfaces of the cylindrical tube, this corresponds to a net flow of energy W − Q across the boundary to the surroundings. There has to be a counterbalancing change to conserve the total energy U.
ΔU = Q − W
in the internal energy of the gas. The first law provides a kind of strict energy accounting system in which the change in the energy account (ΔU) equals the difference between deposits (Q) and withdrawals (W).
There is an important distinction between the quantity ΔU and the related energy quantities Q and W. Because the internal energy U is characterized totally by the quantities (or parameters) that uniquely determine the state of the system at equilibrium, it is said to be a state function such that any change in energy is determined totally by the initial (i) and final (f) states of the system: ΔU = Uf − Ui. However, Q and W are not state functions. Just as in the example of a bursting balloon, the gas inside might do no work in reaching its final expanded state, or it could do maximum work by expanding inside a cylindrical tube with a movable piston to reach the very same final state. All that is required is that the change in energy (ΔU) remains the same. For example, the same change in one’s bank account could be achieved by many different combinations of deposits and withdrawals. Therefore, Q and W are not state functions since their values rely on the certain process (or path) connecting the very same initial and final states. Equally, as it is more significant to speak of the equilibrium in one’s bank account than its deposit or withdrawal content, it is just significant to speak of the internal energy of a system and not its heat or work content.
The classic example of a heat engine is a heavy steam engine, although all modern-day engines adhere to the same principles. Heavy steam engines operate cyclically, with the piston moving up and down once for every cycle. Hot, high-pressure steam is admitted to the cylindrical tube in the first half of each cycle, and afterward, it is allowed to escape once more in the second half. The overall impact is to take heat Q1 generated by burning a fuel to make steam, convert part of it to work, and exhaust the remaining heat Q2 to the environment at a lower temperature level. The net heat energy absorbed is after that Q = Q1 − Q2. Because the engine returns to its initial state, its internal energy U does not change (ΔU = 0). Therefore, by the very first law of thermodynamics, the work done for each complete cycle has to be W = Q1 − Q2. In other words, the work done for each complete cycle is just the difference between the heat Q1 absorbed by the engine at a high temperature and the heat Q2 exhausted at a lower temperature level. The power of thermodynamics is that this conclusion is completely independent of the detailed working mechanism of the engine. It depends only on the overall energy conservation, with heat considered a form of energy.
To save money on fuel and prevent polluting the atmosphere with waste heat, engines are designed to take full advantage of the conversion of absorbed heat Q1 right into useful work and reduce the waste heat Q2. The Carnot efficiency (η) of an engine is defined as the ratio W/Q1 i.e., the fraction of Q1 converted into work. Since W = Q1 − Q2, the efficiency also can be expressed in the form:Suppose there was no waste heat at all; Q2 = 0 and also η = 1, corresponding to 100 percent efficiency. While reducing friction in an engine decreases waste heat, it can never eliminate it; as a result, there is a limitation on exactly how small Q2 can be and, therefore, on exactly how large the efficiency can be.
Isothermal and Adiabatic Process
Since heat engines might undergo a complicated sequence of steps, a simplified model is often utilized to illustrate the principles of thermodynamics. Particularly, think about a gas that expands and contracts within a cylindrical tube with a movable piston under a recommended set of conditions. There are two particularly important sets of requirements. One state, referred to as an isothermal expansion, involves keeping the gas at a constant temperature level. As the gas does work against the restraining force of the piston, it should absorb heat to conserve energy. Otherwise, it would certainly cool down as it expands (or, conversely, heat as it is compressed). It is an example of how the heat absorbed is converted right into work with 100 percent effectiveness. However, the process does not violate fundamental limitations on the point since a single expansion by itself is not a cyclic process.
The second condition referred to as an adiabatic expansion (derived from the Greek Word ‘Adiabatos’, meaning “Impassable”), is one in which the cylindrical tube is assumed to be perfectly insulated to ensure that no heat can flow right into or out of the cylindrical tube. In this instance, the gas cools down as it expands because, by the first law, the work done against the restraining force on the piston can originate from the internal energy of the gas. Therefore, the modification in the internal energy of the gas should be ΔU = − W, as shown by a decrease in its temperature level. Although there is no heat flow, the gas cools down since it is working at the expanse of its internal energy. It can calculate the specific amount of air conditioning from the heat capacity of the gas.
Several natural phenomena are effectively adiabatic since there is insufficient time for significant heat flow. For example, when warm air rises in the atmosphere, it expands and cools down as the pressure drops with altitude; however, the air is a good thermal insulator; therefore, there is no significant heat flow from the surrounding air. In this situation, the surrounding air plays the role of both the insulated cylindrical tube wall surfaces and also the movable piston. The warm air does work against the pressure provided by the surrounding air as it expands; therefore, its temperature level has to go down. A more detailed analysis of this adiabatic expansion explains most of the decrease in temperature level with altitude, accounting for the fact that it is cooler at the top of a mountain than at its base.