Environmental Engineering Reference
In-Depth Information
power generated per hectare of cropland. (c) If electric power is sold at 0.03 $/kWh, calculate the
annual income, per hectare of land, from electricity sales of this biomass energy.
Problem 7.3
A large oak tree produces 2.2 tons of wood in 50 years of growth. The tree has a canopy of 10 m
in diameter, and it collects solar energy for six months each year at an average rate of 177 W/m
2
.
What is the tree's efficiency for converting solar energy to wood heating value? (Assume a wood
heating value of 20 MJ/kg.)
Problem 7.4
Draw a schematic diagram for a geothermal heat pump that works to supply space heat in winter
and air conditioning in summer, and explain how it works.
Problem 7.5
The rate of heat
q
collected by a flat plate solar collector is given by equation (7.2). According
to the limits of the second law of thermodynamics, the maximum electric power
p
m
that could be
generated from this heat flux
q
would be lower by the factor (1
, where
T
c
and
T
a
are the
temperatures of the collector fluid and the atmosphere, respectively. (a) Derive an expression for
the temperature ratio
T
c
/
−
T
a
/
T
c
)
T
a
that will maximize
p
m
, in terms of the collector parameters
β
I
and
U
,
and the temperature
T
a
. (b) Calculate the numerical values of
T
c
/
T
a
,
T
c
, and
p
m
when
β
=
0
.
8,
900 W/m
2
,
5 W/m
2
K, and
T
a
=
I
=
U
=
300 K.
Problem 7.6
Calculate the collector surface area
A
required to heat 500 liters of water a day from 15
◦
Cto80
◦
C
under conditions where the daily insolation on a slanted collector is 1.13 E(7) J/m
2
, assuming 33%
collector efficiency.
Problem 7.7
Explain why a solar flat plate collector used for domestic water heating can work even in subfreezing
ambient temperatures.
Problem 7.8
A spherically focusing solar collector is being designed to generate electric power from a heat
engine, similar to that shown in Figure 7.9. For this design,
β
=
0
.
9, the design solar irradiance is
700 W/m
2
, and the concentration ratio is
CR
I
=
=
2000. Assuming that the heat loss rate from the
T
c
collector,
U(
T
c
−
T
a
)
, is equal to the black-body radiation from the collector, or
σ
(where
σ
is the
Stefan-Boltzmann constant [see Table A.3]), calculate the maximum collector temperature,
(
T
c
)
max
.