Page 36 - Low Temperature Energy Systems with Applications of Renewable Energy

Principles and operation of refrigeration and heat pump systems 25

Table 1.1 has also been modified to include data on the dead state and the specific
exergy for each state point; it is given below as Table 1.2. The dead state has been cho-

sen as 25 C and 0.10 MPa, a common choice. Notice that the exergy at states 1 and 2
are both positive although they have a temperature less than the dead-state tempera-
ture. All states other than the dead state have positive exergy values because there
is a potential for performing work by bringing the state into equilibrium with the
dead state regardless of whether the state lies above or below the dead state.
The temperature of the heated space, T hs , receiving the heat discharged at the
condenser and the temperature of the low-temperature heat source, T 0 , for the evapo-
rator must be specified to allow the exergy terms associated with those heat transfers to
be calculated. Let us assume that the condenser heat is delivered to a reservoir at

T hs ¼ 80 C (353.15 K) and that the evaporator receives heat from the surroundings

at the dead-state temperature, T 0 ¼ 25 C (298.15 K). The exergy accounting for the
system and its components may now be carried out.
Compressor: The compressor receives 140.0 kW of mechanical power all of which
is exergy. The exergy accounting, Eq. (1.20), yields:

_
_
DE C ¼ W C þ _ me 2 _ me 3 ¼ 140 þ 1:8024 ð57:98 125:12Þ¼ 18:99 kW
Condenser: The exergy associated with the heat transfer from the R152a to the heat-
ed space can be seen as two distinct processes: process 3-d and process d-4. The exergy
for the isothermal condensing portion, process d-4, is easily found from Eq. (1.18):

_ T 0 _ 298:15
E Q CNc ¼ 1 Q ¼ 1 1:8024 ð403:59 536:28Þ
c
T c 373:15
¼ 48:07 kW
The negative sign means exergy is being transferred out of the R152a, in the same
direction as the heat transfer. The exergy for the variable-temperature desuperheating
portion may be found by integrating Eq. (1.18) over the process 3-d. Refprop was used
to determine the points along the isobar; a 2nd-order polynomial is an excellent fitto
the data that gives T ds as a function of S, and simple integration yields the following
result:

Z
s d
_ T 0 _ T 0 _
E Q CNds ¼ 1 Q ¼ 1 T ds dS
ds
T ds T ds
s 3
Z Z
s d s d
_ _
¼ T ds dS T 0 dSy 61.45 þ 47:64
s 3 s 3
¼ 13.81 kW
Thus, the sum of these two terms gives the magnitude of the total exergy discharged
_
with the condensing heat E Q CN , as about 61.88 kW. The exergy destroyed in the
condenser, from Eq. (1.21), is: