Overview of thermodynamics
• The science of thermodynamics covers various
concepts and laws describing the conversion of
one form of energy to another, e.g., conversion of
heat energy into mechanical energy as in a steam
or gas turbine or conversion of chemical energy
into heat energy as observed during the
combustion of fuel.
Laws of thermodynamics
1. First law of thermodynamics
In a cyclic process, since the initial and final states are
identical, the net quantity of heat delivered to the
system is proportional to the net quantity of work
done by the system. When heat and work are
mutually convertible, we have the first law of
thermodynamics. Mathematically speaking,
where
Q = Heat supplied to the system,
W =Work done by the system.
The steady-state equation
Where
C is velocity of the mass at inlet or exit
Z is elevation at inlet or exit
g is acceleration due to gravity
Neglecting the effects of kinetic and potential energies
Eq. 1.2 reduces to
when a system passes through a cyclic process
U2 = U1 and Q = W
….(1.3)
The change in the internal energy of the system may be
expressed as dU, the change in heat flow as dQ, and the
change in net work done as dW. Accordingly Eq. 1.3
changes to:
dU = dQ - dW
……(1.4)
In a constant pressure process, dW = pdV
where p is pressure and dV represents the change in volume
of the system on completion of the process, Eq. 1.4
changes to:
dU = dQ - pdV
or,
dQ =dU + pdV
(1.5)
Since p is constant, pdV = d(pV), therefore, Eq. 1.5 may be written
as
dQ = dU + d(pV)
or,
dQ = d(U + pV)
(1.5)
In thermodynamics the quantity (U + pV) occurs frequently, and is
identified with a special property called enthalpy H. Therefore,
dQ =dH
(1.7)
Following the above expression of enthalpy, the specific
enthalpy (enthalpy per unit mass), represented by h in
thermodynamics, is expressed in a state of equilibrium as
h = u + pv
(1.8)
for an isentropic process changes to
dh = vdp
(1.9)
Integrating Eq. 1.9 between state 2 and
state 1 it is found that
h2 - h1 ≈ v(p2 - p1)
(1.10)
Second law of thermodynamics
Concept of entropy:
Mathematically expressed as:
dS = dQ/T
Integrating Eq. 1.14
∫dQ/T = (S2 - S1)
where
S = Entropy of the system
Q= Heat supplied to the system
T = Temperature of the system
(1.14)
(1.15)
From Eqs. 1.14 and 1.15 we may note that for a
adiabatic process dQ = 0, dS = 0 and for an
isothermal process T = T2 =T1 and
Q = T (S2 - S1).
Combining Eq. 1.7 and Eq. 1.14,
dS = dH/T
or,
dH = TdS
(1.16)
or,
per unit mass
dh + Tds
(1.17)
Classification Of Power Plant Cycle
• Power plants cycle generally divided in to the
following groups:
(1) Vapour Power Cycle (Carnot cycle, Rankine
cycle, Regenerative cycle, Reheat cycle, Binary
vapour cycle)
(2) Gas Power Cycles (Otto cycle, Diesel cycle,
Dual combustion cycle, Gas turbine cycle.)
Steam Power Plant
Important definitions:
Saturation temperature: is the temperature a pure
substance start boiling at certain pressure, this
pressure is called saturation pressure.
Saturated liquid: if a pure substance exists as
liquid at saturation temperature and pressure, it
is called saturated liquid.
Wet mixture: is the mixture of liquid and its vapor.
• Saturated vapor: if a pure substance exists as
vapor at saturated temperature and pressure,
it is called saturated vapor.
• Moisture content: is the ratio of liquid mass to
the total mass (mass of liquid and mass of
vapor).
• Dryness fracture (x): is a ratio of vapor mass to
the total mass.
vf : specific volume of saturated liquid.
vg : specific volume of saturated vapor.
vfg : difference between vg and vf (that is ,
vfg= vg- vf
• Enthalpy of vaporization (hfg): or latent heat of
vaporization, It represent the amount of energy
needed to vaporize a unit mass of saturated
liquid at a given temperature or pressure.
• Super heated vapor: When the temperature of
the vapor is higher than the saturated
temperature of this vapor is called super heated
vapor.
• Enthalpy of water (hf): is the enthalpy of heat
absorbed by unit mass of water at constant
pressure until it reaches to the temperature of
vapor forming from (0 °C).
• Enthalpy of dry steam (hg): is the quantity of
heat which needed to change unit mass of water
at (0ºC) to dry steam.
• Specific volume of wet steam:
v = vf + x vfg
1. CARNOT CYCLE
This cycle is of great value to heat power theory
although it has not been possible to construct a
practical plant on this cycle. It has high
thermodynamics efficiency. It is a standard of
comparison for all other cycles. The thermal
efficiency (η) of Carnot cycle is as follows:
• In P-V (Pressure-Volume) and T-S (TemperatureEntropy) diagrams (Figure 1.5) the cycle is
represented by an area bounded by the following
two isothermals and two adiabatic processes:
i. 1-2: Reversible adiabatic expansion
ii. 2-3: Reversible isothermal heat rejection
iii. 3-4: Reversible adiabatic compression
iv. 4-1: Reversible isothermal heat addition.
State 4 in Figure 1.5 refers to saturated liquid and
state 1 refers to saturated vapor.
Example 1.1
Using Figure 1.5, calculate the efficiency and exhaust steam
quality of a steam cycle operating between 4 MPa and
10.13 kPa.
Solution: From the steam table the following values have been
found corresponding to steam pressures 4 MPa and 10.13
kPa:
Example 1.2
Consider the Carnot cycle of Figure 1.5 and calculate the heat
transfers, net work output, cycle efficiency, and specific
steam consumption (s.s.c), using steam operating between
pressures 8 MPa and 9.6 kPa.
Solution: From the steam table the following values have
been found corresponding to steam pressures 8 MPa and
9.6 kPa: