Copyright

The first law of thermodynamics states that energy is conserved; i.e., that energy can be converted from one form to another but cannot be created or destroyed. The first law tells us what forms of energy are involved in a particular energy conversion, but it does not tell us anything about whether the conversion is possible or in which direction the conversion process occurs. Common experience tells us that a boulder naturally falls from a cliff to the ground, but never jumps from the ground to the top of the cliff by itself. The first law does not preclude the boulder from jumping from the ground to the top of the cliff because energy (potential and kinetic) is still conserved in this process. We know by experience that a hot beverage naturally cools as heat is transferred from the beverage to the cool surroundings. The energy lost by the beverage equals the energy gained by the surroundings. The hot beverage will not get hotter, however, because heat flows from a high temperature to a low temperature. The first law does not preclude the beverage from getting hotter in a cool room as long as the energy lost by the room equals the energy gained by the beverage. Experience also tells us that if you drop a raw egg on the floor, it breaks and makes a big gooey mess. The reverse process will not occur; i.e., the shell fragments will not automatically reassemble around the egg white and yolk and then rebound from the floor into your hand. Once again, the first law does not preclude the reverse process from occurring, but the overwhelming experimental evidence tells us that the reverse process does not take place. As a final example, consider the system in Figure 24. A closed tank containing a fluid has a shaft that facilitates the conversion between work and heat. Suppose that we wanted to use this apparatus as a heat engine, a device that converts heat to work. If we were to actually build this device and attempt to raise the weight by transferring heat to the fluid, we would discover that the weight would not be raised. As in the previous examples, the first law does not preclude the conversion of heat to work in this system, but we know from experience that this conversion does not occur.

Based on direct observations of physical systems, it is clear that thermodynamic processes occur only in certain directions. While the first law places no restrictions on the direction in which a thermodynamic process occurs, it does not ensure that the process is possible. To answer that question, we need another thermodynamic principle or law that tells us something about the natural direction of thermodynamic processes. That principle is the second law of thermodynamics. In order for a process to occur, both the first and second laws of thermodynamics must be satisfied. There are various ways of stating the second law of thermodynamics. One of the most useful forms of the second law of thermodynamics, hereafter referred to as simply “the second law”, is that it is impossible for a heat engine to produce an amount of work equal to the amount of heat received from a thermal energy reservoir. In other words, the second law states that it is impossible for a heat engine to convert all the heat it receives from a thermal energy reservoir to work. A heat engine that violates the second law is illustrated in Figure 25. In order to operate, a heat engine must reject some of the heat it receives from the high-temperature source to a low-temperature sink. A heat engine that violates the second law converts 100 percent of this heat to work. This is physically impossible.

The second law can also be stated as no heat engine can have a thermal efficiency of 100 percent. The thermal efficiency of a heat engine, denoted

_th, is defined as the ratio of the work output to the heat input:

Clearly, if the thermal efficiency of a heat engine is 100 percent, Q_in=W_out. If the second law precludes a heat engine from having a thermal efficiency of 100 percent, what is the maximum possible thermal efficiency of a heat engine? As illustrated in Figure 26, a heat engine is a device that converts a portion of the heat supplied to it from a high-temperature source into work. The remaining heat is rejected to a low-temperature sink. The thermal efficiency of a heat engine is given by Equation 6-37. Applying the first law to the heat engine, we obtain

Solving for W_out from Equation 6-38 and substituting the result into Equation 6-37, we obtain

It can be shown mathematically that, for an ideal heat engine operating between source and sink temperatures of T_H and T_L, respectively, the ratio of the heat supplied to the heat rejected equals the ratio of the absolute temperatures of the heat source and heat sink. Thus,

The details of the mathematical proof may be found in most thermodynamics texts. What does it mean for a heat engine to be ideal? The short answer is that a heat engine is considered ideal if the processes within the heat engine itself are reversible. A reversible process is a process that can be reversed in direction without leaving any trace on the surroundings. A simple example of a reversible process is a frictionless pendulum. A frictionless pendulum can swing in either direction without dissipating any heat to the surroundings. A more thorough discussion of this concept may be found in the references at the end of this chapter.

Substituting Equation 6-40 into Equation 6-39, the thermal efficiency for an ideal heat engine becomes

where T_L and T_H denote the absolute temperatures of the low-temperature sink and high-temperature source, respectively. Because T_L and T_H are absolute temperatures, these quantities must be expressed in units of kelvin (K) or rankine (°R). The thermal efficiency given by Equation 6-41 is the maximum possible thermal efficiency a heat engine can have, and is often referred to as the Carnot efficiency, in honor of the French engineer, Sadi Carnot. A heat engine whose thermal efficiency is given by Equation 6-41 is a theoretical heat engine only, an idealization that engineers use to compare with real heat engines. No real heat engine can have a thermal efficiency greater than the Carnot efficiency because no real heat engine is reversible. Hence, the efficiencies of real heat engines, such as steam power plants, should not be compared to 100 percent. Instead, they should be compared to the Carnot efficiency for a heat engine operating between the same temperature limits. The Carnot efficiency is the theoretical upper limit for the thermal efficiency of a heat engine. If a heat engine is purported to have a thermal efficiency greater than the Carnot efficiency, the heat engine is in violation of the second law of thermodynamics.

The first and second laws of thermodynamics are the quintessential governing principles on which all energy processes are based. To summarize: The first law says you can't get something for nothing. The second law says you can't even come close.

Application: Evaluating a Claim for a New Heat Engine

In a patent application for a new heat engine, an inventor claims that the device produces 1 kJ of work for every 1.8 kJ of heat supplied to it. In the application, the inventor states that the heat engine absorbs energy from a 350°C source and rejects energy to a 25°C sink. Evaluate this claim.

The feasibility of the new heat engine may be checked by ascertaining whether the heat engine violates either the first or second laws of thermodynamics. If the first law is violated, the heat engine would have to produce an amount of work greater than the amount of heat supplied to it. Because W_out< Q_in (1 kJ<1.8 kJ) for this heat engine, the first law is satisfied. If the second law is violated, the heat engine would have to have a thermal efficiency greater than the Carnot efficiency for a heat engine operating between the same temperature limits. The actual thermal efficiency of the heat engine is

Noting that the source and sink temperatures must be expressed in absolute units, the Carnot efficiency is

The actual thermal efficiency of the heat engine is greater than the Carnot efficiency (0.556>0.522), so the inventors's claim is invalid. It is physically impossible for this heat engine to produce 1 kJ of work for every 1.8 kJ of heat supplied to it given the source and sink temperatures specified in the patent application.

Earlier in this section we mentioned that there are various ways of stating the second law of thermodynamics. The primary objective of science is to explain the universe in which we live. The second law of thermodynamics, while very useful for analyzing and designing engineering systems, is a scientific principle that has profound consequences. From a scientific standpoint, the second law is considered an “arrow of time” , an immutable principle that assigns a natural direction to all physical processes. Stones fall from cliffs, but never the reverse. Heat flows from hot objects to cold objects, but never the reverse. Raw eggs dropped to the floor make a gooey mess. Cream mixes with coffee, but once mixed, the coffee and cream do not separate back out. Physical processes are ordered-they follow the arrow of time. Matter spreads, energy spreads, reducing the quality of things. According to the second law, things naturally move from order to disorder, from a higher quality to a lower quality, from a more useful state to a less useful state. In short, the second law says that, left to themselves, things get worse. As shown in Figure 27, the second law seems to apply to everything, not just energy systems.

. The second law of thermodynamics has taken its toll on this structure.

The Second Law of Thermodynamics

Objectives

Application: Evaluating a Claim for a New Heat Engine

Practice!