01 basics of thermodynamics
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Basics of Thermodynamics
August 2007Lumut Power
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Time schedule
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First law of thermodynamics dU = dQ - dW In a closed system, entire heat input
can not be converted completely towork.
Defines property Internal Energy (U) Constant Volume Process dW = 0.
Internal energy (U) Depends on
Molecular mass Temperature Atomic motion
High temperature means high internalenergy
Water and Steam - Properties of steam
E = mv2
/2
Molecules are in constant random motion frequently collide with each other and withwalls of contact surface. Internal energy is the total kinetic energy of movingmolecules and the potential energy of vibrating and electrical energy of molecules.
Heating of liquid or vapor increases the internal kinetic energy and therebyincreases the internal energy.
At Saturation phase of steam, when water is converted to vapor, the specificvolume increases. This causes high atomic motion and hence increase ininternal energy.
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Thermodynamic system
Basic steady flow energyequation m1 (U + Pv +V
2/2 + Zg)1 + Q = m2(U+ Pv +V2/2 + Zg)2 + W
U = Internal energy
Pv = Pressure x Volume(termed as Flow work)
V2 /2 = Kinetic energy
Zg = Potential energy
W = Work done by the system
Q = Heat input to the system
U + Pv = Enthalpy (H)
Enthalpy is term formed bycombining the internal energy andflow work together - Analysis of anysystem boundary involves these twoforms of energy and hence this iscombined to produce a meaningfulterm.
Application Steam Flow Energy Equation
Steam Boiler (Heat Exchanger)
Work (w) = 0;
Zg and (V2/2) are very small compared to other components in theequation and can be neglected;
Q = H2 H1
Steam Turbine
Heat Loss (Q) is small compared to other components and hence can
be neglected.Zg = 0 as in general the turbine is mounted in horizontal plane.
(V2/2) is not significant for most of the turbine stages.
W = H2 H1
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Application of steady flow energy equation
0
2
2
2
1
21
12
=
=
=
W
negligibleVV
neglibilegZgZ
TCQ
hhQ
p
Heat Exchanger
Enthalpy Drop across the heat
exchanger contributes for the heattransfer of the fluid in the heat
exchanger.
m1 * (U + Pv +V2/2 + Zg) + Q = m2 * (U+ Pv +V2/2 + Zg) + W
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Application of steady flow energy equation
0
2
2
2
1
21
12
=
=
Q
NegligibleVV
neglibilegZgZ
hhW
m1 * (U + Pv +V2/2 + Zg) + Q = m2 * (U+ Pv +V2/2 + Zg)+ W
Steam Turbine
Enthalpy Drop across the Steam
Turbine is the energy converted
into work
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Application of steady flow energy equation
0
0
2
2
2
1
21
12
=
=
=
W
Q
NegligibleVV
neglibilegZgZ
hh
m1 * (U + Pv +V2/2 + Zg) + Q = m2 * (U+ Pv +V2/2 + Zg) + W
Pressure Reducing Process / Throttling
Enthalpy at inlet of the pressure
reducing valve is same as the at
outlet . No heat loss across thepressure reducing valve
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Water and Steam - Properties of steam
A system with negligible change in kinetic energy andpotential energy and for closed system,
U2 + W= Q + U1 Simplified first law of thermodynamics U = Internal energy W = Work done by the system 1
2 Pdv Q = Heat input to the system
Heat Input = Mass x Specific heat x Temperature For Constant Pressure Process,
W = P (V2 V1) Q = m Cp (T2 T1) = (U2 + PV2) (U1 + PV1) = H2 H1
For Constant Volume Process, W = 0 Q = m Cv (T2 T1) = (U2) (U1)
Enthalpy
Change in enthalpy of fluid can be expressed as Mass x Specific Heat Capacity (atConst Pr.) x Temperature Diff for the constant pressure process.
For air and combustion gas, the zero enthalpy is referred to 27 Deg C and 1.01325Bar as per United States Boiler Industry.
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Water and Steam - Properties of steam
Entropy (S)
Defines the irreversibility of the process Measure of disorderliness of the system Defines a practical boundary of possible work and heat transfer in a process
Change in entropy (system and surrounding) of the irreversible process is alwayspositive
Reduction in entropy in a process is impossible S2 S1 = Cv ln (T2/T1) + R ln (V2/V1)
= Cp ln (T2/T1) + R ln (P2/P1)
=2
1T
QS rev
Reversible Process
Reversible thermodynamic process exist only in theory.
Reversible thermodynamic process concept serve as a limiting case for theheat flow and work flow in any process.
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Steam table (T-S chart)
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Steam Table (Mollier chart)
Enthalpy
(Btu/lb)
Entropy (Btu/lbF)
Entropy (Btu/lbF)
Enthalpy
(Btu/lb)
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Sample Steam table
Properties of Superheated Steam (Pressure)
Interpolation of the steam parameter for dryness fraction X in the saturation phase:
Enthalpy (H) = Hf + X * (Hfg)
Entropy (S) =Sf + X * (Sfg)
Internal Energy (U) = Uf + X * (Ufg)
Volume (v) = vf + X * vfg
Interpolation of the steam parameter for the temperature T and Pressure P in theSuperheated Region when parameter at T1, P and T2, P are known:
Enthalpy (HP,T) = HP,T1 + (HP,T2 - HP,T1)/(T2- T1)
Entropy (SP,T) = SP,T1 + (SP,T2 - SP,T1)/(T2- T1)
Internal Energy (UP,T) = UP,T1 + (UP,T2 - UP,T1)/(T2- T1)
Volume (vP,T) = vP,T1 + (vP,T2 - vP,T1)/(T2- T1)
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Thermodynamic cycle - Carnot Cycle
1 2
34
1 2
34
Isothermal
heat addition
IsentropicExpansion
Isothermalheat rejection
IsentropicCompression
Entropy
Temperature
Practically impossible to construct aengine that works on Carnot cycle.
All process are reversible process.
Defines the maximum possibleefficiency of engine that operates betweenthe same source and sink temperature.
carnot = (T1 T2 )/ T1
T1
T2
Isothermal heat addition of single phase fluid could not be achieved practically.
Isentropic compression of two phase fluid would have problem in wet compression.
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Thermodynamic cycle - Brayton Cycle
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Thermodynamic cycle - Rankine Cycle
Process: b c : Heat input
c d : Expansion work
d a : Condensing (heatrejection) a b : Pump Work
Simple ranking cycle is a fully condensing cycle.
Cycle efficiency is lower with higher heat rejection in the condenser. Condenserloss is a major loss in the Rankine cycle.
Higher temperature and pressure at turbine inlet enable more power generation forthe same heat input and improves cycle efficiency.
Lower the condenser pressure higher the power generation.
Closed cycle can have better vacuum than the open cycle condenser vacuum.
Source temperature (T1) in the above cycle is the mean temperature of the processb-a and the Sink temperature (T
2) is the mean temperature of the process d-a.
Maximum achievable efficiency = (T1-T2)/T1
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Thermodynamic cycle - Combined Cycle