Government Engineering College, Patan MECHANICAL- THIRD SEMESTER(2014-2015) SUBJECT:- ENGINEERING THERMODYNAMICS CHAPTER:- SECOND LAW OF THERMODYNAMICS GUIDED BY:-PROF. M.G.PATEL

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TOPICS INTRODUCTION HEAT ENGINES HEAT PUMP AND REFRIGERATIONS KELVIN STATEMENT CLAUSIUS STATEMENT EQUIVALENCE OF THE CLAUSIUS AND KELVIN STATEMENTS SECOND KIND OF PERPETUAL MOTION MACHINES CARNOT CYCEL CARNOT THEOREM COROLLARY OF CARNOT THEOREM THERMODYNAMIC TEMPERATURE SCALE

SECOND LAW OF THERMODYNAMICS

INTRODUCTION:- The Second Law of Thermodynamics: We observe that heat always flows spontaneously from a warmer object to a cooler one, although the opposite would not violate the conservation of energy. This direction of heat flow is one of the ways of expressing the second law of thermodynamics: The Second Law of Thermodynamics: When objects of different temperatures are brought into thermal contact, the spontaneous flow of heat that results is always from the high temperature object to the low temperature object. Spontaneous heat flow never proceeds in the reverse direction.

HEAT ENGINES

A heat engine is a device that absorbs heat (Q) and uses it to do useful work (W) on the surroundings when operating in a cycle. Sources of heat include the combustion of coal, petroleum or carbohydrates and nuclear reactions. Working substance: the matter inside the heat engine that undergoes addition or rejection of heat and that does work on the surroundings. Examples include air and water vapour (steam). In a cycle, the working substance is in the same thermodynamic state at the end as at the start.

Cold Body (absorbs heat) Heat Engine Hot Body (source of heat) Q1 E W Cold Body (absorbs heat) Q2

Efficiency of a Heat Engine Efficiency, h = Work out/Heat in: Apply First Law to the working substance: DU = Q1 – Q2 – W But in a cycle, DU = 0 Thus, W = Q1 – Q2. Substituting: Lesson: h is maximum when Q2 is minimum.

Example of a Heat Engine Open system

HEAT PUMP AND REFRIGERATIONS

Refrigerator: A heat engine operating in reverse Hot Body Q1 Refrigerator Efficiency: E W Q2 Cold Body

The transfer of heat from a low-temperature region to a high-temperature one requires special devices called refrigerators. Refrigerators and heat pumps are essentially the same devices; they differ in their objectives only.

KELVIN-CLAUSIUS STATEMENT

Kelvin statement of the second law: There is no process whose only effect is to accept heat from a single heat reservoir and transform it entirely into work. Lord Kelvin (William Thomson) (1824-1907)

Note the careful wording: Kelvin statement of the second law: x Note the careful wording: Kelvin statement of the second law: There is no process whose only effect is to accept heat from a single heat reservoir and transform it entirely into work. T=const Why is this no contradiction Because: Transformation of heat work is not the only effect (piston moved) Note: In a cyclic process engine remains unchanged only Alternative Kelvin statement:

Clausius statement of the second Law: There is no process whose only effect is to accept heat from a colder reservoir and transform it to a hotter one. Rudolf Clausius (2.1.1822 -24.8.1888)

Clausius statement of the second law: There is no process whose only effect is to accept heat from a colder reservoir and transform it to a hotter one. Again: A refrigerator accepts heat from a colder reservoir and transfers heat to the hotter reservoir Why is this no contradiction Because: This is not the only thing a refrigerator does. It uses electrical or mechanical energy. Alternative Clausius statement:-

Equivalence of the Clausius and Kelvin statements Logical structure of the proof of equivalence: possibility I II III IV Kelvin-statement true false true false Clausius-statement true true false false We show: 1 Kelvin-statement false Clausius-statement false Clausius-statement false Kelvin-statement false 2 The decision between possibility I and IV is made by experimental experience

Kelvin-statement false There is a non-Kelvin engine 1 Kelvin-statement false There is a non-Kelvin engine Let’s combine this non-Kelvin engine with a heat pump (which we know to exist) There is a non-Clausius engine Clausius-statement false

Clausius-statement false There is a non-Clausius engine 2 Clausius-statement false There is a non-Clausius engine Let’s combine this non-Clausius engine with a heat engine (which we know to exist) There is a non-Kelvin engine Kelvin-statement false

SECOND KIND of Perpetual Motion Machines

A perpetual motion machine of the second kind is a machine which spontaneously converts thermal energy into mechanical work. When the thermal energy is equivalent to the work done, this does not violate the law of conservation of energy. However it does violate the more subtle second law of thermodynamics. The signature of a perpetual motion machine of the second kind is that there is only one heat reservoir involved, which is being spontaneously cooled without involving a transfer of heat to a cooler reservoir. This conversion of heat into useful work, without any side effect, is impossible, according to the second law of thermodynamics.

CARNOT CYCEL

Carnot Cycle Hot Reservoir T1 Cold Reservoir T2 Q1 C W Q2

Pressure T1 Carnot Cycle • a b Q1 Q=0 T2 • c Q=0 • d Q2 Volume

Pressure T1 Carnot Cycle • a b Q1 W Q=0 T2 • c Q=0 • d Q2 Volume

From a to b: isothermal, so that DU = 0 and Q = - W Thus, Q1 = +nRT1ln(Vb/Va) (+ve quantity) From b to c: adiabatic, Q = 0, so that TVg-1 is constant. Thus, T1Vbg-1 = T2Vcg-1 or Similarly, from c to d: isothermal, so that DU = 0 and Q = - W Thus, Q2 = +nRT2ln(Vd/Vc) = -nRT2ln(Vc/Vd) (-ve) Similarly, d to a: adiabatic, Q = 0, so that TVg-1 is constant. Thus, T2Vdg-1 = T1Vag-1 or

But as the volume ratios are equal: We see that: Which means that Now also: But as the volume ratios are equal: This is an important result. Temperature can be defined (on the absolute (Kelvin) scale) in terms of the heat flows in a Carnot Cycle.

What’s Special about a Carnot Cycle? (1) Heat is transferred to/from only two reservoirs at fixed temperatures, T1 and T2 - not at a variety of temperatures. (2) Heat transfer is the most efficient possible because the temperature of the working substance equals the temperature of the reservoirs. No heat is wasted in flowing from hot to cold. (3) The cycle uses an adiabatic process to raise and lower the temperature of the working substance. No heat is wasted in heating up the working substance. (4) Carnot cycles are reversible. Not all cycles are!

What’s Special about a Carnot Cycle? (5) The Carnot theorem states that the Carnot cycle (or any reversible cycle) is the most efficient cycle possible. The Carnot cycle defines an upper limit to the efficiency of a cycle. • Recall that for any cycle, the efficiency of a heat engine is given as: • For an engine using a Carnot cycle, the efficiency is also equal to: • Where T1 and T2 are the temperatures of the hot and cold reservoirs, respectively, in degrees Kelvin.  As T2 > 0, hc is always <1.

CARNOT THEOREM:- No engine operating between two reservoirs can be more efficient than a Carnot engine operating between the same two reservoirs.

COROLLARY OF CARNOT THEOREM

• Let’s first consider Fig • Let’s first consider Fig. (a) where we have our Carnot engine (with eC, Qh*, W* and Qc*)and our super-engine (with e, Qh, W and Qc), and run them so that they produce the same work W = W*.

• Now that we have our terms figured out, in Fig • Now that we have our terms figured out, in Fig. (b) we use our super-engine to drivethe Carnot engine backwards, as a Carnot refrigerator. So our super-engine takes Qhfrom the hot reservoir, puts Qc into the cold reservoir and feeds work W into theCarnot refrigerator, which then takes Qc* from the cold reservoir and puts Qh* into thehot reservoir.

• In Fig. (c) we show the net effect of this combination, it acts as a refrigerator taking heat Qc* − Qc > 0 into the engine and with no work input, puts heat Qh* − Qh > 0 into thehot reservoir. But this is illegal according to Clausius statement of the second law.Hence e can only be less than or equal to eC, proving Carnot’s theorem. On top of that, it might also be clear why some people also call it Carnot’s statement of the second law. Even though it doesn’t talk about the second law specifically, it is as intimately linked to it as the Kelvin-Planck and Clausius statements are.

THERMODYNAMIC TEMPERATURE SCALE

It is possible to define a temperature scale in a independent way of the used thermometric substance Temperature of the boiling point of sulfur measured with constant-volume gas thermometers . P100 is the pressure of the gas at 100ºC

The ideal-gas temperature scale is defined so that the temperature of the triple point state is 273.16 kelvins, K. The triple point of water is the unique temperature and pressure at which water, water vapor and ice coexist in equilibrium. [0.01 ºC and 4.58 mmHg]

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