FIRST LAW APPLIED TO ENGINEERING SYSTEMS
Here the first law of thermodynamics applied to different engineering systems is discussed. It is
assumed in general that the processes are of steady flow type and so the steady flow energy
equation can be directly used with modifications in it.
Turbine
It is the device in which the high temperature and high pressure fluid is expanded to low
temperature and pressure resulting in generation of positive work at turbine shaft. Thus, turbine is a
work producing device. A turbine is hence a device in which work is done by the fluid on a set of
rotating blades. As a result there is a pressure drop from the inlet to the outlet of the turbine. In
some situations there may be heat transferred from the device to the surroundings, but often the
heat transfer is negligible. In steam, gas, or hydroelectric power plants, the device that drives the
electric generator is the turbine.
Turbines using gas as working fluid are called gas turbine where as turbines using steam are called
steam turbines. Expansion in turbine is assumed to be of adiabatic type so that the maximum
amount of work is produced.
Heat transfer from turbines is usually negligible (Q=0) since they are typically well insulated.
Assuming change in kinetic energy, potential energy to be negligible, the steady flow energy
equation can be modified and written between 1 and 2 as,
Ein = Eout
O + mh1 = WT + mh2
WT = m(h1 – h2)
i.e., Q = 0 and total energy interaction is available in the form of work
Turbine work = m (h1 – h2) = m cp(T1 – T2)
Here m is mass flow rate and T1, T2 are temperatures at inlet and outlet.
Figure 1: Turbine
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Compressor
Compressor is a work absorbing device used for increasing the pressure of a fluid. Pressure of a fluid
is increased by doing work upon it, which is accompanied by increase in temperature depending on
the gas properties. Work is supplied to the compressor devices from an external source through a
rotating shaft. Therefore, compressors involve work inputs.
Figure 2: Compressor
For compression of a gas adiabatic process is used as in this there is no heat loss and so minimum
work requirement. Let us assume change in kinetic energy and potential energy to be negligible
between 1 & 2 and also flow to be of steady type.
Applying steady flow energy equation in modified form:
Q=0
ΔKE = 0
ΔPE = 0
Wc = (–ve) work for compression
mh1 = – Wc + mh2
or
Wc = m(h2 – h1)
Adiabatic compression work = m(h2 – h1) = mcp (T2 – T1)
Here T1, T2 are temperatures at inlet and outlet and m is mass flow rate.
Pump
A pump is used for pumping liquid or suction of liquid. In case of pump the following assumptions
can be made:
(i) Heat transfer is zero, Q = 0
(ii) Change in internal energy is zero, ΔU = 0
Therefore
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Figure 3: Pump
Boiler
A boiler is the engineering device used for steam generation at constant pressure. Heat is supplied
externally to the boiler for steam generation depending upon state of steam desired. Boiler may be
assumed similar to a closed vessel having no work interaction, no change in kinetic energy, no
change in potential energy.
i.e.
W = 0, ΔKE = 0, ΔPE = 0.
Applying steady flow energy equation
Qboiler + m(h1) = m(h2)
or
Qboiler = m(h2 – h1) = m cp (T2 – T1)
Figure 4: Boiler
Condenser
Condenser is the device used for condensing vapour into liquid at constant pressure. It is a type of
heat exchanger in which another cool fluid is used for condensing the vapours into liquid. Heat
exchange between the hot fluid and cold fluid takes place indirectly as cold fluid passes through the
tubes and hot vapours are outside tubes in the shell.
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Figure 5: Condensor
Steady flow energy equation can be applied with the following assumptions:
(i) No work interaction, W = 0
(ii) No change in kinetic energy, ΔKE = 0
(iii) No change in potential energy, ΔPE = 0
Heat lost by steam,
Q = m (h1 – h2)
Nozzles and Diffusers
A nozzle is a device that is used to increase the velocity of a flowing fluid. It does this by reducing the
pressure. A diffuser is a device that increases the pressure in a flowing fluid by reducing the velocity.
There is no work input into the devices and usually negligible heat transfer. Assumptions are
negligible internal energy and potential energy changes.
In case of a nozzle as the enthalpy of the fluid decreases and pressure drops simultaneously the flow
of fluid is accelerated. This is generally used to convert the part of the energy of steam into kinetic
energy of steam supplied to the turbine.
Figure 6: Steam nozzle
For the system:
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Δ PE = 0
W=0
Q =0
Applying the energy equation to the system,
ℎ1 +
𝑢22
2
or
−
𝑢12
2
= ℎ1 − ℎ2
or
𝑢12
𝑢22
= ℎ2 +
2
2
𝑢22 − 𝑢12 = 2 (ℎ1 − ℎ2 )
𝑢22 = 𝑢12 + 2 (ℎ1 − ℎ2 )
𝑢2 = √𝑢12 + 2(ℎ1 − ℎ1 )
where velocity u is in m/s and enthalpy h in joules
if
u1 << u2, then
Three equations may be used for nozzle and diffuser flow: energy, continuity, and a process
equation, such as for an adiabatic quasiequilibrium (intermediate steps in the process are all close to
equilibrium) flow. Thus, we may have three unknowns at the exit, given the entering conditions.
There may also be shock waves in supersonic flows or “choked” subsonic flows. These more
complicated flows are included in a compressible flow course.
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HEAT EXCHANGERS
Heat exchangers are used to transfer energy from a hotter body to a colder body or to the
surroundings by means of heat transfer. Energy is transferred from the hot gases after combustion
in a power plant to the water in the pipes of the boiler, and from the hot water that leaves an
automobile engine to the atmosphere by use of a radiator. Many heat exchangers utilize a flow
passage into which a fluid enters and from which the fluid exits at a different temperature. The
velocity does not normally change, the pressure drop through the passage is usually neglected, and
the potential energy change is assumed zero. The energy equation then results in
𝑄̇ = 𝑚̇(ℎ2 − ℎ1 )
Energy may be exchanged between two moving fluids, as shown schematically in Figure 6. For a
control volume including the combined unit, which is assumed to be insulated, the energy equation,
as applied to the control volume of Figure 6a, would be
0 = 𝑚𝐴̇ (ℎ𝐴2 − ℎ𝐴1 ) + 𝑚̇𝐵 (ℎ𝐵2 − ℎ𝐵1 )
The energy that leaves fluid A is transferred to fluid B by means of the heat transfer 𝑄̇ . For the
control volumes shown in Figure 6, we have
𝑄̇ = 𝑚𝐵̇ (ℎ𝐵2 − ℎ𝐵1 )
-𝑄̇ = 𝑚𝐴̇ (ℎ𝐴2 − ℎ𝐴1 )
Figure 6: heat exchanger (a) Combined unit
(b) Separated control volumes
Throttling devices
Throttling refers to passage of a fluid through some restricted opening under isenthalpic conditions.
Thus in the figure shown below the fluid passes through a restriction from section 1 to 2 and
undergoes drop in its pressure and increase in volume, but during this passage enthalpy remains
constant, such that h1 = h2.
Based on above throttling process the device called “throttle valve” has been developed in which
pressure drop is realized without involving any work and heat interaction, change in kinetic energy
and potential energy. Temperature may drop or increase during the throttling process and shall
depend upon the Joule-Thomson coefficient, a property based on characteristic of substance.
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Figure 7: Throttling device
Throttling valves are usually small devices, and the flow through them may be assumed to be
adiabatic (Q= 0) since there is neither sufficient time nor large enough area for any effective heat
transfer to take place. Also, there is no work done (W= 0), and the change in potential energy, if any,
is very small (ΔPE=0). Even though the exit velocity is often considerably higher than the inlet
velocity, in many cases, the increase in kinetic energy s insignificant (ΔKE=0). Then the conservation
of energy equation for this single-stream steady-flow device reduces to:
h2=h1
(kJ/kg)
That is, enthalpy values at the inlet and exit of a throttling valve are the same. For this reason, a
throttling valve is sometimes called an isenthalpic device. Note, however, that for throttling devices
with large exposed surface areas such as capillary tubes, heat transfer may be significant. To gain
some insight into how throttling affects fluid properties:
U1 + P1V1= U2 +P2V2
or
Internal energy + Flow energy = Constant
Thus the final outcome of a throttling process depends on which of the two quantities increases
during the process. If the flow energy increases during the process (P2V2 > P1V1), it can do so at the
expense of the internal energy. As a result, internal energy decreases, which is usually accompanied
by a drop in temperature. If the product PV decreases, the internal energy and the temperature of a
fluid will increase during a throttling process. In the case of an ideal gas, h= h(T), and thus the
temperature has to remain constant during a throttling process as shown in Figure 8.
Figure 8: The temperature of an ideal gas does not change during a throttling (h = constant) process
since h = h(T).
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Tutorial
1. Air at 100 kPa and 280 K is compressed steadily to 600 kPa and 400 K. The mass flow rate of
the air is 0.02 kg/s, and a heat loss of 16 kJ/kg occurs during the process. Assuming the
changes in kinetic and potential energies are negligible, determine the necessary power
input to the compressor.
Figure 9: Compressor
2. Air flows through the supersonic nozzle shown. The inlet conditions are 7 kPa and 420°C.
The nozzle exit diameter is adjusted such that the exiting velocity is 700 m/s. Calculate (a)
the exit temperature, (b) the mass flow rate, and (c) the exit diameter. Assume an adiabatic
quasiequilibrium flow.
Figure 10: Nozzle
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