
THERMODYNAMICS  THEORY



Thermal Reservoirs

Atmosphere, Land , and Water in a Lake are Examples
of Thermal Reservoirs
Source and Sink


A thermal reservoir is a specific kind of system with a
large thermal energy capacity that can supply or absorb finite
amounts of heat and always remains at constant temperature. Such a system
can be approximated in a number of ways:
 Large land masses
 Earth's atmosphere
 Large bodies of water: oceans, lakes, or rivers
 Any physical body whose thermal energy capacity is large relative
to the amount of energy it supplies or absorbs, for example, a large
block of ice
A reservoir that supplies energy in the form of heat is called a source
and one that absorbs energy in the form of heat is called a sink. For example,
atmospheric air is a source for heat pumps and a sink for air conditioners.



Energy Analysis of Cycles



When a system in a given initial
state experiences a series of quasiequilibrium processes and returns
to its initial state, the system undergoes a
cycle. The energy balance for any system undergoing a cycle takes the form
ΔE_{cycle} = Q_{cycle}  W_{cycle}
where
Q_{cycle} = the net amount
of energy transferred
by
heat for
the cycle,
Q_{cycle} = Q_{in} Q_{out}
W_{cycle} = the net amount
of energy transferred
by work for the cycle,
W_{cycle} = W_{out }
W_{in}
Notice that the directions of the heat and work are indicated
by the subscripts in and out. Therefore, Q_{in}, Q_{out},
W_{out}, and W_{in }are all positive numbers.






Since the system is returned to its initial state after the cycle,
there is no net change in its energy. Therefore,
ΔE_{cycle} =
0
Then the equation reduces to
Q_{cycle} = W_{cycle}
This expression can satisfy every thermodynamic cycle, regardless
of the sequence of processes followed by the system undergoing the
cycle or the nature of the substances making up the system.
If the system undergoing cycles delivers a net work to its surroundings
during each cycle, the cycle is called a power cycle.
W_{cycle} = Q_{in} 
Q_{out}
On the other hand, if the system needs work input from the surroundings
to run each cycle, the cycle is called a refrigeration and heat pump
cycle.
W_{cycle} = Q_{out} 
Q_{in}
where W_{cycle } has a positive value.






Heat Engine



Most people understand that work can always be converted to
heat directly and completely. But converting heat to work requires
the use
of special devices. These devices are called heat engines.
Heat engines operate on a cycle and receive heat from a hightemperature
source, convert part of this heat to work, and then reject the remaining
waste heat
to a
lowtemperature sink during the cycle.
A steam power plant is an example of heat engine. The schematic
of a basic steam power plant is shown on the left. The cycle is:
 Heat
(Q_{in}) is transferred to the steam in the boiler from
a furnace, which is the energy
source.
 The turbine produces work (W_{out} ) when steam passes
through it.
 A condenser
transfers the waste heat (Q_{out}) from steam to the
energy sink, such as the atmosphere.
 A
pump is used to carry the water from the condenser back to the
boiler. Work (W_{in}) is required to compress water to boiler
pressure.
The net work output from this power plant is the difference between
the work output and the work input.
W_{net, out} = W_{out}  W_{in }
From the energy balance of the cycle, the net work output is
W_{net, out} = Q_{in}  Q_{out
}






Thermal Efficiency



A heat engine can only convert part of the energy it received
from the source to work. A certain amount of heat is dissipated to
the sink
as waste heat.
The fraction of the heat input that is converted to net work output is
a measure of the performance of a heat engine and is called the thermal
efficiency(η_{th}). In general, the
efficiency (or performance) can be expressed in terms of the desired
output and the required input as
Performance = Desired output/ Required input
For heat engines, the desired output is the net work output (W_{net,
out}) and
the required input is the heat input( Q_{in}). Hence the thermal
efficiency of a heat engine can be expressed as
Thermal efficiency = Net work output/Heat input
or
η_{th}= W_{net, out}/Q_{in}
Since W_{net, out} = Q_{in}  Q_{out} , it
can be rewritten as
η_{th}=
(Q_{in} Q_{out})/Q_{in
} = 1  Q_{out}/Q_{in}
To bring uniformity to the treatment of heat engines, refrigerators,
and heat pumps (wIll be introduced in the following paragraph), Q_{H} and
Q_{L} are
defined as
 Q_{H} equals the amount of heat transferred between the
device (heat engines, refrigerators, and heat pumps) and
a thermal reservoir of high temperature T_{H }.
 Q_{L} equals the amount of heat transferred between the
device (heat engines, refrigerators, and heat pumps) and a thermal
reservoir
of low temperature
T_{L}.
Note that Q_{H} and Q_{L} are all positive numbers.
Hence, the thermal efficiency for any heat engine is:
η_{th}= W_{net, out}/Q_{H} = (Q_{H}
Q_{L})/Q_{H } =
1  Q_{L}/Q_{H}
Note that for heat engine, Q_{L} is always less than Q_{H
},and η_{th
} is always less than 1.






For refrigerators or heat pumps, the efficiency is in terms of the
coefficient of performance (COP). A subscript R is used to denote refrigerators
(COP_{R}) and HP for heat pumps (COP_{HP}).
A refrigerator
is used to remove heat (Q_{L}) from a lower temperature space
with an electric work input (W_{net,in}), then dissipates
the total energy from the heat input and
the electric work (Q_{H}) to a higher temperature thermal reservoir.
Hence, the desired output is Q_{L} and
the
required
input
is
W_{net,
in}.
So the COP_{R} can be expressed as
COP_{R} = Heat removed
/Net work input
=
Q_{L} / W_{net, in}
= Q_{L} /( Q_{H} Q_{L})
= 1/(Q_{H}/Q_{L}1)






A heat pump is a device which transfers heat
from a lowtemperature medium to a hightemperature one. For example,
a
heat pump is used to heat a room in winter, which transfer heat from
the lowtemperature outdoor air to the hightemperature air inside
the room. Hence, the desired output is the heat transferred to the
room (Q_{H}). Also, a net work input (W_{net, in})
is necessary. The COP_{HP} can be expressed as
COP_{R} = Heat delivered/Required
work input
=
Q_{H} / W_{net, in}
=
Q_{H} /( Q_{H} Q_{L})
=
1/(1Q_{L}/Q_{H}) 



