Thermal Efficiency Apparatus
012-05443A
6
Power Delivered to the Hot Reservoir (P
H
)
The hot reservoir is maintained at a constant temperature
by running a current through a resistor. Since the resis-
tance changes with temperature, it is necessary to mea-
sure the current and the voltage to obtain the power input.
Then P
H
= I
H
V
H
.
Power Dissipated by the Load Resistor (P
W
)
The power dissipated by the load resistor is determined
by measuring the voltage drop across the known load
resistance and using the formula
P
W
=
V
2
R
.
The load resistors have a tolerance of 1%.
➤
NOTE: We may use the equation
P
W
=
V
2
R
for
measuring the power in the load resistor because
the temperature (and therefore resistance) of this
resistor does not change significantly. We may not
use this equation to measure power in the heating
resistor, since its temperature (and resistance)
changes.
When the Thermal Efficiency Apparatus is operated as a
heat pump rather than as a heat engine, the load resistors
are not used so it is necessary to measure both the current
and the voltage. So the current into the Peltier device is
measured with an ammeter, and the voltage across the
Peltier device is measured with a voltmeter and the power
input is calculated with the formula P
W
= I
W
V
W
.
Indirect Measurements
It will be necessary to know three additional quantities in
the experiments:
➀
The internal resistance of the Peltier
device;
➁
The amount of heat conducted through the
device and the amount radiated away;
➂
The amount of
heat pumped from the cold reservoir. These quantities
may be determined indirectly with the Thermal Effi-
ciency Apparatus in the following ways.
Internal Resistance
Before the adjusted efficiency can be calculated, it is
necessary to calculate the internal resistance. This is
accomplished by measuring the voltage drop across the
Peltier device when an external load is applied.
First run the Thermal Efficiency Apparatus with a load
resistor (R) as in figure 6. The electrical equivalent of this
setup is shown in figure 5. Kirchoff’s Loop Rule gives
V
S
– Ir – IR = 0
Next, run the Thermal Efficiency Apparatus with no load,
as in Figure 7. Since there is no current flowing through
the internal resistance of the Peltier Device, the voltage
drop across the internal resistance is zero and the voltage
measured will just be V
S
.
Since we have measured V
w
rather than I in the heat
engine mode, the equation above becomes
V
s
–
V
w
R
r – V
w
= 0
Solving this for the internal resistance gives us
r =
V
s
– V
w
V
w
R
.
You may also find the resistance by measuring the
currents for two different load resistors and then solving
the resulting loop rule equations simultaneously.
Heat Conduction and Radiation
The heat that leaves the hot reservoir goes two places:
part of it is actually available to be used by the heat
engine to do work while the other part bypasses the
engine either by being radiated away from the hot
reservoir or by being conducted through the Peltier device
to the cold side. The portion of the heat which bypasses
the engine by radiation and conduction would be trans-
ferred in this same manner whether or not the device is
connected to a load and the heat engine is doing work.
The Thermal Efficiency Apparatus is run with a load
connected to measure P
H
(Figure 6) and then the load is
disconnected and the power input into the hot reservoir is
adjusted to maintain the temperatures (less power is needed
when there is no load since less heat is being drawn from
the hot reservoir). See Figure 7. P
H(open)
is the power input
Figure 5: Procedure for Finding Internal Resistance
V
s
r
R
l
V
l
Peltier Device
