ME 166 Applied Thermodynamics - The 2nd Law PDF

Kwame Nkrumah University of Science & Technology, Kumasi, Ghana ME 166 Applied Thermodynamics - The 2nd Law D. A. QUANSAH SECOND LAW OF THERMODYNAMICS The second law of thermodynamics continues where the first law...

Kwame Nkrumah University of Science & Technology, Kumasi, Ghana ME 166 Applied Thermodynamics - The 2nd Law D. A. QUANSAH SECOND LAW OF THERMODYNAMICS The second law of thermodynamics continues where the first law stops, and helps us establish the direction of particular processes. – heat flows from a hot body to a cold one. – rubber bands unwind. – fluid flows from a high-pressure region to a low-pressure region. The first law of thermodynamics relates several variables involved in a physical process, but does not give any information as to the direction of the process. www.knust.edu.gh www.knust.edu.gh  HEAT ENGINES, HEAT PUMPS, AND REFRIGERATORS Cyclic devices are either heat pumps, heat engines or refrigerators and operate between two thermal reservoirs. Thermal reservoirs are entities that are capable of providing or accepting heat without changing temperatures. E.g. atmosphere, lakes and furnaces. www.knust.edu.gh www.knust.edu.gh  HEAT ENGINES A heat engine is defined as a device that converts heat energy into mechanical energy. TH and TL are the temperatures of the source and sink respectively. QH is the heat transfer from the high temp reservoir and QL the heat transfer to the low temp reservoir. www.knust.edu.gh www.knust.edu.gh  HEAT ENGINES The net work output is given as: – First law for cyclic processes, Net Work = Net Heat. The performance of a heat engine is the thermal efficiency: www.knust.edu.gh www.knust.edu.gh  HEAT PUMPS A heat pump is a device that moves heat from one location (heat source) at a lower temperature to another location (heat sink) at a higher temperature using mechanical work. QH = W + QL The measure of performance of a heat pump is the Coefficient of Performance (COP). www.knust.edu.gh www.knust.edu.gh  REFRIGERATORS Refrigerators, like, heat pumps move heat from a cooler region to a hotter one with the input of work. Refrig. Note - each of the performance measures represents: 𝑸𝑳 𝑪𝑶𝑷𝑹𝒆𝒇𝒓𝒊𝒈 = Desired Output 𝑾 Performance = Required Input COPh.p = COPrefrig+1 www.knust.edu.gh www.knust.edu.gh STATEMENTS OF THE SECOND LAW There are a number of statements of the 2nd Law, two are presented: Clausius Statement: It is impossible to construct a device that operates in a cycle and whose sole effect is the transfer of Not possible! heat from a cooler body to a hotter body. www.knust.edu.gh www.knust.edu.gh  STATEMENTS OF THE SECOND LAW Kelvin-Planck Statement: It is impossible to construct a device that operates in a cycle and produces no other effect than the production of work and the transfer of heat from a single body. – It is impossible to construct a heat engine that extracts energy from a Not possible! reservoir, does work, and does not transfer heat to a low-temperature reservoir. www.knust.edu.gh www.knust.edu.gh  REVERSIBILITY A reversible process is defined as a process which, having taken place, can be reversed and in so doing leaves no change in either the system or the surroundings. A reversible engine is an engine that operates with reversible processes only. – A reversible engine is most efficient engine that can possibly be constructed. www.knust.edu.gh www.knust.edu.gh  REVERSIBILITY The process has to be a quasi-equilibrium process; and: – No friction is involved in the process. – Heat transfer occurs due to an infinitesimal temperature difference only. – Unrestrained expansion does not occur. Losses such as those due to friction and others listed above are referred to as irreversibilities. www.knust.edu.gh www.knust.edu.gh  REVERSIBILITY Some sources of irreversibilities: Friction Unrestrained expansion Mixing of two gases Heat transfer across finite temperature difference Electric resistance Inelastic deformation of solids, and Chemical reaction  THE CARNOT ENGINE The Carnot Engine is an ideal engine that uses reversible processes to form its cycle of operation; thus it is also called a reversible engine. The efficiency of the Carnot engine establishes the maximum possible efficiency of any real engine. www.knust.edu.gh www.knust.edu.gh  THE CARNOT ENGINE 1 → 2: Isothermal expansion. 2 → 3: Adiabatic reversible expansion. 3 → 4: Isothermal compression. 4 → 1: Adiabatic reversible compression. www.knust.edu.gh www.knust.edu.gh  THE CARNOT ENGINE Applying the first law to the cycle: The thermal efficiency is then written as: Postulates based on the Carnot engine: Postulate 1: It is impossible to construct an engine, operating between two given temperature reservoirs, that is more efficient than the Carnot engine. Postulate 2: The efficiency of a Carnot engine is not dependent on the working substance used or any particular design feature of the engine. Postulate 3: All reversible engines, operating between two given temperature reservoirs, have the same efficiency as a Carnot engine operating between the same two temperature reservoirs. www.knust.edu.gh www.knust.edu.gh  THE CARNOT ENGINE CARNOT EFFICIENCY: Isothermal expansion Adiabatic expansion Isothermal compression Adiabatic expansion www.knust.edu.gh www.knust.edu.gh  THE CARNOT ENGINE The coefficient of performance for a Carnot heat pump becomes The coefficient of performance for a Carnot refrigerator takes the form The above measures of performance set limits that real devices can only approach. www.knust.edu.gh www.knust.edu.gh  Entropy Changes Enthropy is a quantitative measure of randomness. Consider an infinitesimal isothermal expansion by an ideal gas. An amount of heat dQ is added and the gas expands by a small amount dV such that the gas Temperature is kept constant. Recall: internal energy remains constant, since it depends only on temperature. From the first law, one may write: 𝑛𝑅𝑇 𝑑𝑉 𝑑𝑄 𝑑𝑄 = 𝑑𝑊 = 𝑝𝑑𝑉 = 𝑑𝑉 = 𝑉 𝑉 𝑛𝑅𝑇 The gas is obviously more disordered after expansion than before, i.e. increased randomness due to volume for mobility. 𝑑𝑉 𝑑𝑄 The fractional change in volume is a measure of randomness and is proportional to. 𝑉 𝑇 The symbol S is introduced for entropy of the system. The infinitesimal entropy change ds for an infinitesimal reversible process at temperature T is given as: 𝑑𝑄 𝑑𝑆 = www.knust.edu.gh 𝑇 www.knust.edu.gh  Entropy Changes– Worked Example Enthropy is a quantitative measure of randomness. Consider an infinitesimal isothermal expansion by an ideal gas. An amount of heat dQ is added and the gas expands by a small amount dV such that the gas Temperature is kept constant. Recall: internal energy remains constant, since it depends only on temperature. From the first law, one may write: 𝑛𝑅𝑇 𝑑𝑉 𝑑𝑄 𝑑𝑄 = 𝑑𝑊 = 𝑝𝑑𝑉 = 𝑑𝑉 = 𝑉 𝑉 𝑛𝑅𝑇 The gas is obviously more disordered after expansion than before, i.e. increased randomness due to volume for mobility. 𝑑𝑉 𝑑𝑄 The fractional change in volume is a measure of randomness and is proportional to. 𝑉 𝑇 The symbol S is introduced for entropy of the system. The infinitesimal entropy change ds for an infinitesimal reversible process at temperature T is given as: 𝑑𝑄 𝑑𝑆 = 𝑇 www.knust.edu.gh www.knust.edu.gh  Entropy Changes– Worked Example If an amount of heat Q is added during a reversible isothermal process at absolute temperature T, the total entropy change ΔS is given by: Q Δ𝑆 = 𝑆2 − 𝑆1 = (reversible isothermal process) T Entropy has unit of J/K. 2 Q Δ𝑆 = න (for any reversible process) T 1 Where 1 and 2 represent initial and final states of the system. Note that entropy is a point function. www.knust.edu.gh www.knust.edu.gh  Entropy Changes– Worked Example Consider a reversible Carnot heat engine, the entropy change for the cycle For a reversible cyclic process: න 𝑑𝑄 = 0 may written as: 𝑇 𝑄𝐻 𝑄𝐿 − =0 𝑑𝑄 𝑇𝐻 𝑇𝐿 For a irreversible cyclic process: න < 0 𝑇 For an irreversible cycle, less work will be extracted and 𝑄 𝐿_𝑖𝑟𝑟 > 𝑄 𝐿. Recall: the Clausius inequality: ර 𝑑𝑄 ≤ 0 𝑇 Consequently: 𝑄𝐻 𝑄𝐿_𝑖𝑟𝑟 −