## SAT Physics Thermodynamics - Heat Engines

HEAT ENGINES
A heat engine is a device that converts thermal energy into other forms of energy. Heat engines operate between a high temperature (hot), TH, and a low temperature (cold), TC. Heat QH is added into the engine at high temperature. Heat QC is removed from the engine at low temperature. The heat transferred into the engine is greater than the heat removed from the engine, QH > Qc. The difference in energy can be used to do useful work, W.
W= Qh - Qc
An analogy would be using a waterfall to turn a paddle wheel. Figure 19.3 compares the waterfall on the left to a heat engine on the right.

Figure 19.3. Energy flow in heat engines

Efficiency
The heat added to an engine, QH, can be thought of as thermal fuel. The heat removed from the engine, Qc, can be thought of as thermal exhaust. Engine exhaust is not ideal, especially in a world concerned with pollution and dwindling resources. However, no heat engine can operate without expending some waste heat, Qc, at low temperature, Tc. The warm engine of a car after it has been running is an example of low-temperature (Tc) waste heat (Qc). This is the heat from gasoline that was not used to propel the car forward. Engine efficiency is the relationship between the total (net) work, Wnet, produced by an engine to the heat added, QH. Efficiency measures useful output compared with input. Miles per gallon is a type of efficiency. It is a ratio of the car’s useful output (miles traveled) to input (fuel). The efficiency, e, of a heat engine is also a ratio of output (net work) to input (heat added). Efficiencies are calculated using absolute values, and they are expressed as percentages.
Heat engines have a theoretical maximum efficiency. This is calculated using the temperature extremes, TH and Tc, between which the engine operates. The best possible efficiency of a heat engine is calculated as follows:
Calculations with this formula require Kelvin temperatures. Real engines have efficiencies that are lower than this theoretical best-case efficiency.

Efficiency of a Heat Engine
An engine operates between 27°C and 127°C. Determine its theoretical efficiency.

WHAT'S THE TRICK?

When temperatures are given, work in the Kelvin scale and use the following formula:

ENTROPY
The natural flow of heat is from high temperature to low temperature. Systems with different temperatures contain particles that are moving at different average speeds. When these systems mix, all types of collisions occur. However, mathematical probability drives the direction of heat transfer. The warmer system has more fast-moving particles, while the cooler system has more slow-moving particles. Therefore, collisions between fast particles and slow particles are more likely. In these collisions, energy is transferred from the fast particles to the slow particles, Energy continues to transfer until both systems have the same average particle speeds. Therefore, the equilibrium state is the statistically most probable state that can occur.
Entropy is a way to quantify the probability of finding a system in a particular state. Figure 19.4(a), below, shows two gases separated by a movable wall. The gas in the left compartment initially has more molecules than the gas in the right compartment. Figures 19.4(b) and 19.4(c) show two possible states that the system can be found in after the wall has been removed.
Figures 19.4(b) and 19.4(c) are snapshots of the system at an instant in time. The gas particles are in random motion, and both of the resulting diagrams are actually possible. However, the highly organized pattern in Figure 19.4(b) is about as likely as winning millions in a lottery. It has a low probability, and therefore it has low entropy. Random states like the one seen in Figure 19.4(c) are statistically more likely to occur. They are more probable and thus have higher entropy. Probability drives systems toward random and disordered equilibrium states with higher entropy. Therefore, entropy is associated with messiness or randomness. The more random a system is, the greater its entropy. In addition, the natural trend is toward equilibrium and toward greater entropy.
Look again at Figure 19.4(c), the most probable result when the wall was removed. What is the likelihood that the molecules in Figure 19.4(c) will spontaneously separate back into their original compartments, returning to their locations in Figure 19.4(a), and then remain in those positions without a wall to hold them? This scenario is not likely and does not take place. This means that removing the wall is an irreversible step. Entropy drives thermodynamic processes toward equilibrium. It ensures that isolated (no environmental interference) thermal processes are irreversible.
Heat engines increase entropy. When gasoline is added into a car, the gasoline is actually large, organized, high-energy molecules with low entropy. During combustion, the gasoline is turned into water vapor and carbon dioxide. These molecules are smaller, less organized, and less energetic. The combustion reaction has increased the entropy of the system. When these molecules leave the exhaust pipe of the car, they spread throughout the atmosphere, further increasing disorder and entropy. Is it possible for these molecules to find each other and to re-form into the original molecules of gasoline? No. Entropy is associated with probability, which favors irreversible randomness.

SECOND LAW OF THERMODYNAMICS
The second law of thermodynamics addresses entropy, the drive toward equilibrium and its irreversible nature.
• The entropy of an isolated system cannot decrease.
• The entropy of isolated systems always increases until the system reaches equilibrium.
• Once at equilibrium, the entropy of the system remains constant.
An isolated system is a system that follows natural tendencies and does not interact with the surrounding environment. When systems are not isolated, natural tendencies may be reversed as long as energy is supplied to the system by the environment. For example, the natural tendency is for a waterfall to flow downward. This can be reversed. As the Sun’s radiant energy is added to the water, the water rises through evaporation to continue the water cycle. The environment must expend a great deal of energy in an effort to interfere with the natural tendency of the system. The energy required to carry the water to the top of the waterfall is greater than the amount of energy that will be released when the water falls on its own.
A heat pump is a thermodynamic device that acts like the Sun’s radiant energy evaporating the water to continue the water cycle. Without the Sun, ultimately all of Earth’s water would flow down from all elevations into the oceans. A heat pump transfers heat opposite the natural direction of natural heat flow. A heat pump moves heat from low temperature to high temperature. Like the waterfall analogy, a heat pump must add more energy to move heat the wrong direction than would be transferred if heat moved from a region of high temperature to a region of low temperature on its own.
The following general trends are consequences of entropy and the second law of thermodynamics.
• The natural tendency is for systems to move to equilibrium and for entropy (disorder) to increase.
• When systems with different temperatures come into contact, heat flows spontaneously from the high-temperature region to the low-temperature region until thermal equilibrium is reached.
• Heat engines can never be 100% efficient.
• Heat pumps reverse entropy and move heat from a low-temperature region to a high- temperature region. This requires the addition of energy from the environment. The energy that must be added is greater than the energy that would be released if heat flowed normally.

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