7/29/2019 MM211 lec12
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23/09/20
Temperature-Entropy cycle
(Rankine Cycle) As per first law of thermo, we can present
effect of P and V on a fluid, which is compressed and expanded
in a closed cycle on PV diagram.
Similarly T and thermal energy or entropy S can be used to
represent expansion and contraction of a gas ina closed loop. The
gas circulates in the heat engine absorbing heat from high T
reservoir, passes through amachine to convert some of this thermal
energy into work and discharging some heat to the lowtemperature
reservoir. T-S diagram can be used to present this process.
If water is taken as fluid , which is boiled at T H (path1-2) in
a steam
boiler, which is then passed through an adiabatic and reversible
expander
(turbine). The change in entropy or S is zero upon passing
through turbine.
Thus path 2-3 isentropic. Heat is then exchanged with condenser
at TL in
passing though 3-4. Here the steam is condensed into liquid
water, which is
then pumped isentropically back into the cycle through 4-1 path
to the boiler.
The pump is run by the part of the work output of the turbine.
This is a basic
Version of an ideal Rankine cycle. Here, the work done is
also
Wrev
= -QH(T
H-T
L)/T
H
The Rankine cycle is the fundamental operating cycle of all
power
plants where an operating fluid is continuously evaporated
and
condensed.
Entropy
Temp.
TTH
TLS1 S2
1 2
4 3
RefrigeratorsCarnot Cycle in Reverse
machine designed to remove heat from low temperature region and
pump it to ahigher temperature by doing some work on it.
To maintain the temperature to lower value than surrounding, a
household fridgepumps the thermal energy as heat from low
temperature source to high temperaturesink and into the
ambient.
The Clausius statement of the Second Law of Thermodynamics
asserts that it isimpossible to construct a device that, operating
in a cycle, has no effect other thanthe transfer of heat from a
cooler to a hotter body. This means that energy will notflow from
cold to hot regions without outside assistance. The refrigerator
and heat
pump both satisfy the Clausius requirement of external action
through theapplication of mechanical power or equivalent natural
transfers of heat.
The refrigerator cycle is thus reverse of Carnots cycle. The
performance of this cycle is determined by heat removed from
low temperate source divided by the work required.
(QL/Wrev).
This is termed as figure of merit.
refrig= QL /Wrev= TL/(TH-TL)
