Lecture 2

1st law of thermodynamics Cont.,2nd law of thermodynamics,

And Cycles

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Conservation of Mass For a certain control volume

conservation of mass (continuity equation) is:

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And the mass flow rate is given by

Where :

V : velocity (m/s)

A : cross sectional area (m2)

v : specific volume (m3/Kg)

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Example: Air is flowing in a 0.2-m-diameter

pipe at a uniform velocity of 0.1 m/s. The temperature is 25 ºC and the pressure 150 kPa. Determine the mass flow rate.

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Solution

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Nozzle: A nozzle is a steady-state device whose purpose is to

create a high velocity fluid stream at the expense of the fluid’s pressure. It is contoured in an appropriate manner to expand a flowing fluid smoothly to a lower pressure, thereby, increasing its velocity. There is no means to do any work – there are no moving parts. There is little or no change in PE and usually little or no heat transfer

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Diffuser: A steady-state diffuser is a device constructed to

decelerate a high velocity fluid in a manner that results in an increase in pressure of the fluid. In essence, it is the exact opposite of a nozzle, and it may be thought of as fluid flowing in the opposite direction through a nozzle, with the opposite effects.

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Example: Air at 0.6 MPa and 200 ºC enters an

insulated nozzle with a velocity of 50 m/s. It leaves at a pressure of 0.15 MPa and a velocity of 600 m/s. Determine the final temperature of the air.

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Turbine: A turbine is a rotary steady-state machine whose purpose

is to produce shaft work at the expense of the pressure of the working fluid. Two general classes of turbines

Steam turbines, in which the steam exiting the turbine passes to a condenser, where it is condensed to a liquid.

Gas turbines, in which the gas usually exhausts to the atmosphere from the turbine.

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In either type, the turbine exit pressure is fixed by the environment into which the working fluid exhausts, and the turbine inlet pressure has been reached by different ways (boiler, combustion).

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Compressor and Pump: The purpose of a steady-state

compressor (gas) or pump (liquid) is the same: to increase the pressure of a fluid by putting in shaft work. The internal processes are essentially the opposite of the two processes occurring inside a turbine.

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The working fluid enters the compressor at low pressure, moving

into a set of rotation blades, from which it exits at high velocity, a

result of the shaft work input to the fluid

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2nd law of thermodynamics

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The second law acknowledges that processes proceed in a certain direction but not in the opposite direction

Examples: A hot cup of coffee cools by virtue of heat transfer to the surroundings, but heat will not flow from the cooler surroundings to the hotter cup of coffee.

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Gasoline is used as a car drives up a hill, but the fuel level in the gasoline tank cannot be restored to its original level when the car go down the hill.

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Consider the cycle shown, known from our experience to be impossible actually to complete.

These two examples lead us to a consideration of the heat engine and the refrigerator, which is also referred to as a heat pump. With the heat engine we can have a system that operates in a cycle and performs a net positive work and a net positive heat transfer. With the heat pump we can have a system that operates in a cycle and has heat transferred to it from a low-temperature body and heat transferred from it to a high-temp body though work is required to do this.

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A simple steam power plant as a whole may be considered a heat engine. It has a working fluid (steam) to which and from which heat is transferred, and which does a certain amount of work as it undergoes a cycle.

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In general, we say that efficiency is the ratio of output, the energy sought (work), to input, the energy that costs (cost of the fuel). Thermal efficiency is defined as

Typical values for the thermal efficiency of real engines are about 35 – 50 % for large power plants, 30 – 35 % for gasoline engines, and 35 – 40 % for diesel engine.

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The “efficiency” of a refrigerator is expressed in terms of the coefficient of performance

A household refrigerator may have a coefficient of performance (COP) of about 2.5, whereas a deep freeze unit will be closer to 1.0

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The Kelvin-Planck Statement: It is impossible to construct a device that will operate in a cycle and produce no effect other than the raising of a weight and the exchange of heat with a single reservoir.

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The Clausius Statement: It is impossible to construct a device that operates in a cycle and produces no effect other than the transfer of heat from a cooler body to a hotter body. This statement is related to the refrigerator or heat pump. In effect, it states that it is impossible to construct a refrigerator that operates without an input of work. This also implies that the COP is always less than infinity.

The two statements of the second law are equivalent. The truth (violation) of each statement implies the truth (violation) of the other.

Carnot CycleFor an engine working between two reservoirs at different temperatures. It consists of two reversible isothermal and two reversible adiabatic processes. For a cycle 1-2-3-4:1.Undergoes isothermal expansion in 1-2 while absorbing heat from high temperature reservoir 2.Undergoes adiabatic expansion in 2-3 3.Undergoes isothermal compression in 3-4 4.Undergoes adiabatic compression in 4-1.                                                               Heat is transferred to the working material during 1-2 (Q1) and heat is rejected during 3-4 (Q2). The

thermal efficiency is thus ηth = W/Q1. Applying first law, we

have, W = Q1 − Q2, so that ηth = 1 − Q2/Q1.

Carnot's principle states that1. No heat engine working between two thermal reservoirs is more efficient than the Carnot engine, and 2. All Carnot engines working between reservoirs of the same temperature have the same efficiency. The proof by contradiction of the above statements come from the second law, by considering cases where they are violated.

Since T and S are properties, you can use a T-S graph instead of a p-V graph to describe the change in the system undergoing a reversible cycle. We have, from the first law, dQ + dW = 0. Thus the area under the T-S graph is the work done by the system. Further, the reversible adiabatic processes appear as vertical lines in the graph, while the reversible isothermal processes appear as horizontal lines.

Rankine CycleIn the Rankine cycle, also called the standard vapor power cycle, the working fluid follows a closed cycle. We will consider water as a working substance. In the Rankine cycle, water is pumped from a low pressure to a high pressure using a liquid pump. This water is then heated in the boiler at constant pressure where its temperature increases and it is converted to superheated vapor. This vapor is then expanded in an expander to generate work. This expander can be a turbine or a reciprocating (i.e. piston) machine such as those used in older steam locomotive or ship. The output of the expander is then cooled in a condenser to the liquid state and fed to the pump. The Rankine cycle differs from the Carnot cycle in that the input to the pump is a liquid (it is cooled more in the condenser). This allows the use of a small, low power pump due to the lower specific volume of liquid compared to steam. Also, the heat transfer in the boiler takes place mainly as a result of a phase change, compared to the isothermal heating of the ideal gas in the Carnot cycle, so that the efficiency is quite good (even though it is still lower than the Carnot efficiency). The amount of heat transferred as the liquid is heated to its boiling point is very small compared to the heat transfer during phase change. The steam is superheated so that no liquid state exists inside the turbine. Condensation in the turbine can be devastating as it can cause corrosion and erosion of the blades.

Otto Cycle Diesel Cycle

Dual Cycle Gas Turbine Cycle (or Joule-Brayton Cycle)

Refrigeration CyclesThe ideal refrigeration cycle is reverse of Carnot cycle, working as a heat pump instead of as a heat engine.

COP (efficiency) = Ql / W = Tl / (Th – Tl) (for Carnot)

However, there are practical difficulties in making such a system work. The gas refrigeration cycle is used in aircraft to cool cabin air. The ambient air is compressed and then cooled using work from a turbine. The turbine itself uses work from the compressed air, further cooling it. The output of the turbine as well as the air which is used to cool the output of the compressor is mixed and sent to the cabin.

The Rankine vapor-compression cycle is a common alternative to the ideal Carnot cycle

Extra slides

1 .Tube bundle 4.Baffle 7.tube sheet2. Shell Nozzle 5.Vent Nozzle 8.Drain

nozzle3. tube 6.inlet tube side 9.Shell side

1: Heat Exchanger Schematic

Units of Specific Heat

Ckg

J

Cg

cal

Tm

QC

oo

Note that by definition, the specific heat of water is 1 cal/gC.

Material J/kgC cal/gC

Water 4186 1

Ice 2090 0.50

Steam 2010 0.48

Silver 234 0.056

Aluminum 900 0.215

Copper 387 0.0924

Gold 129 0.0308

Iron 448 0.107

Lead 128 0.0305

Brass 380 0.092

Glass 837 0.200

Wood 1700 0.41

Ethyl Alcohol 2400 0.58

Beryllium 1830 0.436

Example Calculation•Compare the amount of heat energy required to

raise the temperature of 1 kg of water and 1 kg of iron 20 C?

calCCgcalg)(Q

calCCgcalg)(Q

TmCQ

oo

oo

2140)20)(/107.0(1000

IronFor

000,20)20)(/1(1000

For Water

Thermodynamics

•4 basic processes:•Isothermal.•Adiabatic.•Isometric.•Isobaric

Carnot Engine-most efficient

Thermodynamic Cycles•A cyclic thermodynamics

process is a closed path on a PV diagram.

•The most efficient thermodynamic cycle is called the Carnot cycle.

•It consists of two adiabats and two

isotherms.

Simplest Heat Engine

Clausius Inequality

Consider Rankine Cycle

B

C1

3

4

P

T

2

P2 = P3 = 1 MPaT2 = 100 CT3 = 350 C

SH vap

Sat liq

x = 1

P1 = P4 = 100 kPa and sat so T = 100 C

T

s

1

2

3

4

cond

boilerturb

180 C

100 C

350 C2a

1.30 7.36

s3 = 7.30

Closed Cycle Open Cycle

Power and Refrigeration Cycle

Rankine Cycle (Two-phase Power Cycle)

Simple steam power plant which operates on the Rankine cycle

9.2 Rankine Cycle

Rankine Cycle

1-2 :Reversible adiabatic pumping (pump)

2-3 :Constant pressure heat addition (boiler)

3-4 :Reversible adiabatic expansion (turbine)

4-1 :Constant pressure heat rejection (condenser)

Heat and work may be represented by various areas

in the T-s diagram. PE and KE negligible.

Carnot Cycle;Pumping of two-phase mixture – difficult!! Superheating at dropping pressure – difficult!!

>-Rankine cycle is the ideal cycle that can be approximated in practice

Rankine Cycle

Reheat

Ideal reheat cycle

9.3 Reheat and Regeneration

Reheat and Regeneration

Ideal regenerative cycle

) Rankine) = (Carnot (w/ reversible heat transfer

>-Impractical heat transfer from turbine

Moisture content from turbine

th th

Reheat and Regeneration

Regenerative cycle with an open feedwater heater

Open Feedwater: Less expensive

Requires a pump between each heaterReheat and Regeneration

Arrangement of regenerative feedwater heaters in an actual power plant

Reheat and Regeneration

Cogeneration

Cogeneration system

)Process steam) + (Electricity(

Reheat and Regeneration

Both Rankine and Brayton Cycles

)Two isobaric processes() +Two isentropic processes(

Two phase : Rankine cycle – Steam Power Plant

Single phase : Brayton cycle – Gas Turbine

9.4 Brayton Cycle

Brayton Cycle

Gas turbine operating on the Brayton cycle

(a)open cycle

(b)closed cycle

Brayton Cycle

Air-Standard Cycle for Jet Propulsion

Ideal gas-turbine for a jet engine

)Brayton cycle)+(Reversible adiabatic nozzle(

9.6 Jet Propulsion Cycle

Jet Propulsion Cycle

Vapor Compression Refrigeration Cycle

Ideal vapor-compression refrigeration cycle

9.8 Vapor Compression Refrigeration Cycle

Vapor Compression Refrigeration Cycle

Single-Phase Power Cycle (Air-Standard Power Cycle)

Brayton cycle – Shaft work, gas turbine

Otto cycle – PdV work, gasoline engine

Diesel cycle – PdV work, Diesel engine

IC engine with an open cycle

>-Approximation by a closed cycle

Combustion replaced by heat transfer

Fixed mass of air as the working fluid

Reheat and Regeneration