THERMODYNAMICS - THEORY
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 quasi-equilibrium processes and returns
to its initial state, the system undergoes a
cycle. The energy balance for any system undergoing a cycle takes the form
ΔEcycle = Qcycle - Wcycle
Qcycle = the net amount
of energy transferred
Qcycle = Qin- Qout
Wcycle = the net amount
of energy transferred
by work for the cycle,
Wcycle = Wout -
Notice that the directions of the heat and work are indicated
by the subscripts in and out. Therefore, Qin, Qout,
Wout, and Win 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,
Then the equation reduces to
Qcycle = Wcycle
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.
Wcycle = Qin -
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
Wcycle = Qout -
where Wcycle has a positive value.
Most people understand that work can always be converted to
heat directly and completely. But converting heat to work requires
of special devices. These devices are called heat engines.
Heat engines operate on a cycle and receive heat from a high-temperature
source, convert part of this heat to work, and then reject the remaining
low-temperature 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:
(Qin) is transferred to the steam in the boiler from
a furnace, which is the energy
- The turbine produces work (Wout ) when steam passes
- A condenser
transfers the waste heat (Qout) from steam to the
energy sink, such as the atmosphere.
pump is used to carry the water from the condenser back to the
boiler. Work (Win) is required to compress water to boiler
The net work output from this power plant is the difference between
the work output and the work input.
Wnet, out = Wout - Win
From the energy balance of the cycle, the net work output is
Wnet, out = Qin - Qout
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
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(ηth). 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 (Wnet,
the required input is the heat input( Qin). Hence the thermal
efficiency of a heat engine can be expressed as
Thermal efficiency = Net work output/Heat input
ηth= Wnet, out/Qin
Since Wnet, out = Qin - Qout , it
can be rewritten as
= 1 - Qout/Qin
To bring uniformity to the treatment of heat engines, refrigerators,
and heat pumps (wIll be introduced in the following paragraph), QH and
- QH equals the amount of heat transferred between the
device (heat engines, refrigerators, and heat pumps) and
a thermal reservoir of high temperature TH .
- QL equals the amount of heat transferred between the
device (heat engines, refrigerators, and heat pumps) and a thermal
of low temperature
Note that QH and QL are all positive numbers.
Hence, the thermal efficiency for any heat engine is:
ηth= Wnet, out/QH = (QH-
1 - QL/QH
Note that for heat engine, QL is always less than QH
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
(COPR) and HP for heat pumps (COPHP).
is used to remove heat (QL) from a lower temperature space
with an electric work input (Wnet,in), then dissipates
the total energy from the heat input and
the electric work (QH) to a higher temperature thermal reservoir.
Hence, the desired output is QL and
So the COPR can be expressed as
COPR = Heat removed
/Net work input
QL / Wnet, in
= QL /( QH- QL)
A heat pump is a device which transfers heat
from a low-temperature medium to a high-temperature one. For example,
heat pump is used to heat a room in winter, which transfer heat from
the low-temperature outdoor air to the high-temperature air inside
the room. Hence, the desired output is the heat transferred to the
room (QH). Also, a net work input (Wnet, in)
is necessary. The COPHP can be expressed as
COPR = Heat delivered/Required
QH / Wnet, in
QH /( QH- QL)