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Chapter 6

# MECH 237 Chapter 6: The Second Law of Thermodynamics Premium

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Department
Mechanical Engineering
Course
MECH 237
Professor
Daniel B.Olsen
Semester
Spring

Description
CHAPTER 6: THE SECOND LAW OF THERMODYNAMICS 6.1 – Introduction to the Second Law • A process cannot occur unless it satisfies both the first and second laws of thermodynamics. • The second law of thermodynamics identifies the direction of the process and als o asserts that energy has quality as well as quantity. • The second law can be used to determine the theoretical limits for systems and the degree of completion of chemical reactions. • The second law can be used to quantify the level of perfection of a proce ss and point the direction to eliminate imperfections effectively. 6.2 – Thermal Energy Reservoirs • Thermal energy reservoir : a hypothetical body with a relatively large thermal energy capacity that can supply or absorb finite amounts of heat without undergo ing any change in temperature. • Thermal energy capacity is defined as mass multiplied by specific heat. • A two –phase system can be modeled as a reservoir since it can absorb and release large quantities of heat while remaining at a constant temperature. • Reservoirs do not have to be large, they can be any body whose thermal energy capacity is large relative to the amount of energy it supplies or absorbs. • Source: a reservoir that supplies energy in the form of heat • Sink: reservoir that absorbs energy in the form of heat. • Heat reservoir: a common name for thermal energy reservoirs since they supply or absorb energy in the form of heat. • Thermal pollution: irresponsible management of waste energy which significantly increases the temperature in the surrounding environment. 6.3 – Heat Engines • Work can easily be converted to other forms of energy, but converting other forms of energy to work is not that easy. • Work can be converted to heat directly and completely • Heat engines: a device required to convert heat to work. All heat engines can be characterized by: o they receive heat from a high-temperature source (solar energy, oil furnace, nuclear reactor, etc.) o They convert part of this heat to work (usually in the form of a rotating shaft) o They reject the remaining waste heat to a low -temperature sink (the atmosphere, rivers, etc.) o The operate on a cycle • Working fluid: a fluid involved in heat engines and other cyclic devices from which heat is transferred to and from while undergoing a cycle. • heat engine is often used in a broad sense to include work -producing devices that do no operate in a thermodynamic cycle • Q inamount of heat supplied to a fluid from a high-temperature source • Q out the amount of heat rejected from a fluid to a low -temperature sink • W out: the amount of work delivered to the system/device • W :inhe amount of work required by the system to perform its function. • The net work output is the difference between the total work output and the total work input W net, outW outW in (kJ) • For a closed system undergoing a cycle, the change in internal energy Δ U is zero • The net work output of the system is also equal to the net heat transfer to the system W net, outQin– Q out (kJ) • In the above equation Q routesents the magnitude of the energy wasted in order to complete the cycle. Q out never zero, thus the net work output of a heat engine is always less than the amount of heat input. And only part of the heat transferred to the heat engine is converted to work. • Thermal efficiency: η the fraction of the heat input that is converted to net work output is as measure of the performance of a heat engine. • for heat engines the desired output is the net work output and the required input if the amount of heat supplied to the working flu id. • Thermal efficiency of a heat engine : ▯▯▯ ▯▯▯▯ ▯▯▯▯▯▯ Thermal efficiency = ▯▯▯▯▯ ▯▯▯▯ ▯▯▯▯▯ Or ▯ ▯▯▯,▯▯▯ ηth= ▯ ▯▯ which can also be expressed as: ▯▯▯▯ ηth 1 - ▯▯▯ • Cyclic devices operate bet ween a high-temperature medium at temperature T and a H low-temperature medium at temperature T L • Q H the magnitude of heat transfer between the cyclic device and the high temperature medium at temperature T H • Q : the magnitude of heat transfer between the cyclic device and the low temperature L medium at temperature T L • Both Q and Q are magnitudes so they will be positive quantities. L H • The net work output and thermal efficiency relations for any heat engine can be expressed as: W net, outQH – QL And ▯ ▯▯▯,▯▯▯ ▯▯ ηth= ▯▯ or th ▯▯ η = 1 - • Thermal efficiency is a measure of how efficiently a heat engine converts the heat that it receives to work. • The thermal efficiency of work -producing devices is relatively low and almost half of the energy supplied to these devices ends up as waste or useless energy • Waste energy: energy that cannot be recycled • Every heat engine must waste some energy by transferring it to a low -temperature reservoir in order to complete the cycle • No heat engine can convert all the heat it receives to useful work and this limitation of thermal efficiency in heat engines forms the basis for the Kelvin -Planck statement. • Kelvin-Planck statement of the second law of thermodynamics : it is impossible for any device that operates on a cycle to receive heat from a single reservoir and produce a net amount of work. • Thus, a heat engine must exchange heat with a low -temperature sink as well as a high- temperature source to keep operating. • The KP statement can also be expressed as: no heat engine can have a thermal efficiency of 100 percent. • Note that the impossibility of having a 100 percent efficient heat engine is not due to friction or other dissipative effects. 6.4: Refrigerators and Heat Pumps • Heat transfers in the direction of decreasing temperature, i.e., from high -temperature mediums to low temperature ones. And this heat transfer does not require any devices. The reverse however, cannot occur on its own. • Refrigerators: like heat engines, are cyclic devices. They transfer heat from a low temperature medium to a high-temperature medium. • Refrigerant: the working fluid used in the refrigeration cycle. • the most frequently used refrigeration cycle is the vapor -compression refrigeration cycle, which involves four main components: a compressor, a condenser, an expansion valve and an evaporator. • Coefficient of performance : (COP) the efficiency of a refrigerator. The objective of a refrigerator is to remove heat (Q L from the refrigerated space. To do this requires work input (W net, inthis can be expressed as: ▯▯▯▯▯▯▯ ▯▯▯▯▯▯ ▯ COP R = ▯ ▯▯▯▯▯▯▯▯ ▯▯▯▯▯ ▯ ▯▯▯,▯▯ • The conservation of energy principle for a cyclic device requires that: W net, inH – Q L (kJ) • The COP relation then becomes: ▯▯ ▯ COP R ▯▯▯▯ ▯ = ▯▯▯ ▯ ▯▯ • COP can be greater than unity meaning that the amount of heat removed from the R refrigerated space can be greater than the amount of work input. o This is in contrast with the thermal efficiency, which can never be greater than 1. • Heat pump: a device that transfers heat from a low-temperature medium to a high temperature one. • refrigerators and heat pumps operate on the same cycle but differ in objectives. • The objective of a refrigerator is to maintain the refrigerated space at a low temperature by removing heat from it. The heat is then discharged to a higher - temperature medium. • The objective of a heat pump is to maintain a heated space at a high temperature. This is done by absorbing heat from a low-temperature source and supplying this heat to the high-temperature medium, such as a house. • The measure of performance of a heat pump is also expressed in terms of coefficient of performance (COP ): HP ▯▯▯▯▯▯▯ ▯▯▯▯▯▯ ▯▯ COP HP ▯▯▯▯▯▯▯▯ ▯▯▯▯▯ = ▯ ▯▯▯,▯▯ COP HP ▯▯ = ▯ ▯▯▯▯ ▯ ▯ ▯▯▯ ▯▯ • Comparing the two COP equations reveals: COP HPCOP + R (for fixed values of QL and Q H • a heat pump will function, at worst, as a resistance heater, supplying as much e nergy to the house as it consumes. • Air conditioners: basically a refrigerator whose refrigerated space is a room or a building • Energy efficiency ratio: (EER) or seasonal energy efficiency ratio (SEER), the measure of performance of air conditioners and h eat pumps. • Clausius Statement: a classical statement of the second law of thermodynamics; it is impossible to construct a device that operates in a cycle and produces no effect other than the transfer of heat from a lower -temperature body to a higher temperature body. • that is, the device must leave a trace on its surroundings. • The Kelvin-Planck and the Clausius statements are equivalent in their consequences and either statement can be used to express the second law of thermodynamics. Any devices that violates the KP statement must also violate the Clausius statement and vice versa. 6.5: Perpetual Motion Machines • A process cannot take place unless it satisfies both the first and second laws of thermodynamics. • Perpetual-Motion machine: any device that violates either the first or second law of thermodynamics, these devices do not work. • Perpetual-motion machine of the first kind : (PMM1) violates the first law of thermodynamics by creating energy • Perpetual-motion machine of the second kind : (PMM2) violates the second law of thermodynamics 6.6: Reversible and Irreversible Processes: • Irreversible processes: once they have taken place, cannot reverse themselves spontaneously and restore the system to its initial state. • Reversible processes: a process that can be reversed without leaving any trace on the surroundings. Both the system and the surroundings are returned to their initial states at the end of the reverse process. • This is possible only if the net heat and net work exchange between the system and t he surroundings is zero for the combined (original and reverse) process. • A system can return to its initial state following a process regardless if it is reversible or irreversible. The only difference is that a reversible process will not leave any net change on the surroundings and a irreversible process will change its surroundings. • Reversible processes do not occur in nature, they are an idealized process. Thus, all processes occurring in nature are irreversible. • Reversible process can be viewed a s theoretical limits for the corresponding irreversible ones. • Second law efficiency: the degree of approximation to the corresponding reversible processes. Enables us to compare
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