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Thermodynamics

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Published in: Physics
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Sufficient for mechanical engineering

Sidhant S / Bathinda

7 years of teaching experience

Qualification: mechanical engineering

Teaches: Geography, History, Mathematics, Science, Mechanical

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  1. Chapter 6 AVAILABLE ENERGY, AVAILABILITY AND IRREVERSIBILITY From second law of thermodynamics we found that complete conversion of heat into work is not possible in a continuous process. Also it has been proved that the most efficient cycle to produce work is a reversible power cycle (Carnot cycle). Even in carnot cycle, the efficiency of conversion can never be unity and hence to establish a comparison of the work-energy conversion in actual processes, the maximum theoretical work obtainable with respect to some datum must be determined. This chapter is dedicated for this objective. 6.1 Available and Unavailable Energy The energy content of a system can be divided into two parts • Available energy, which under ideal conditions may be completely converted into work Unavailable energy which is usually rejected as waste. Consider Q units of heat energy available at a temperature T. Available part of energy can be obtained by assuming that the heat is supplied to a Carnot engine. Work obtained from the Q is the available part. The quantity — Q is the unavailable part. In a carnot engine T-S diagram these quantities can be represented as shown in the fig 6.1. The term To is the ambient temperature. Hence it can be concluded that the available and unavailable part of energy content of a system depends on the ambient conditions also. 6.2 Reversible Work In A Non-flow Process From first law of thermodynamics Qsys w=U2 UI From second law of thermodynamics for a reversible process (As) universe Where (As) system (As) surroundings where, Q system surroundings system 1 surr Surr = To(srsl) Sys ...6.1 ...6.2 ...6.3 substituting in 6.1 we get
  2. To(S2-Sl) w=U2 U (U2 UI) - SO since the process is reversible W can be represented W rev wrev= (UI U2) TO(SF S2) This is also the maximum work in the process. ...6.4 For a closed system, when undergoing change in volume, the work done against the atmospheric pressure: TO(S S2) ...6.5 6.3 But this work is not an useful work and hence max, useful atm max = [(UI 1.12) TO(SI- S2)]- po(V2 VI) = (UI IJ2) + PO(VI Reversible Work In A Steady-state Control Volume Steady flow energy equation for a constant volume is out for a single inlet and outlet From Second law of thermodynamics As universe where As Assur in — + gZ 4) ...6.6
  3. Substituting these values we get Tom(S2 From eqn 6.6 neglecting kinetic and potential energy changes ...6.7 In an open system a fixed volume in space known as control volume is taken for analysis. Hence the atmospheric work term p (VI-V ) should not be considered. Therefore for an open system max,useful rev 6.4 Availability The maximum useful work that can be obtained from the system such that the system comes to a dead state, while exchanging heat only with the surroundings, is known as availability of the system. Here the term dead state means a state where the system is in thermal and mechanical equilibrium with the surroundings. Therefore for a closed system availability can be expressed as similarly for an open system v -(H so In steady flow systems the exit conditions are assumed to be in equilibrium with the surroundings. The change in availability of a system when it moves from one state to another can be given as: for a closed system 42 ...6.10
  4. for an open system 6.5 Availability Change Involving Heat Exchange with Reservoirs ...6.11 Consider a system undergoing a change of state while interacting with a reservoir kept at TR and atmosphere at pressure po and temperature T . Net heat transfer to the system QR 00 System W Rev Qnet= QR-QO From first law of thermodynamics Qnet- Wrev=U2-Ul Reservoir Atmosphere ...6.12 From second law of thermodynamics, assuming the process to be reversible The negative sign for QR shows that the heat is removed from the reservoir. By rearranging We get
  5. Net heat transferred =QR-QO Qnet QR-QR TO(SI S2) Substituting 6.13 in 6.12 we get TO(SI S2) wre U 2 UI UI U2 TO(SI S2)+QR 1 UI S2)+QR 1 nux, useful 6.6 Irreversibility ...6.13 ...6.14 ...6.15 Work obtained in an irreversible process will always be less than that of a reversible process. This difference is termed as irreversibility (i.e) the difference between the reversible work and the actual workfor a given change of state of a system is called irreversibility. act rev Let a stationary closed system receiving Q kJ of heat is giving out W kJ of work. From first law act of thermodynamics. Q-Wact=U2 UI act w rev 1 U2+Q U2) TO(SI SO IJ2) + TO(As) system act rev (UI-U2) Q system = TO(As) Q Where Q = Q = To(As) surroundings surroundings system = TO(As) +T As system O surroundings universe
  6. Since (As) will be positive for an irreversible flow, irreversibility will be zero for a universe reversible process and will never be negative. 1>0 Similarly for a steady flow system Where Therefore rev 1 act — h2) — To O surroundings = TO(SI SO + T As O surroundings = T [AS -FAS surroundings sys = TO [Asu niverse

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