PASCO TD-8564 THERMAL EFFICIENCY APPARATUS - Manual (Page 25)

012-05443A Thermal Efficiency Apparatus
21
Experiment 5: Load for Optimum Performance
EQUIPMENT NEEDED:
— Thermal Efficiency Apparatus
— DCpower supply capable of 2.5 A at 12 V
— 3 kg (7 lbs) ice and a bucket for the ice-water bath
— ohmmeter
— ammeter (up to 3 A)
— 2 voltmeters
— patch cords
Theory
This experiment finds the load resistor which maximizes the power output of the heat
engine. The power delivered to the load resistor, R, is P = I
2 R. The amount of current that
flows through the load resistor varies as the load is varied. From Figure
10, V
S
= I(r+R) where V
S
is the Seebeck voltage and r is the internal resistance of the
Peltier device.
So the power can be expressed in terms of the Seebeck voltage, the internal resistance, and
the load resistance:
P =
V
s
r + R
2
R
Assuming the Seebeck voltage remains constant if the temperatures of the hot and cold
reservoirs are constant, the power can be maximized with respect to the load resistance by
taking the derivative and setting it equal to zero:
dP
dR
=
V
S
2
(r – R)
(r + R)
3
= 0
This shows that when the load resistance is equal to the internal resistance of the Peltier
device, the power delivered to the load will be a maximum.
Place ends
of tubing in
ice water
tub
Connect to appropriate AC supply
(powers pump to circulate ice water) Ω
A
V
Power
supply
V
Figure 5.2 Connecting the 0.5
Ω
load resistor
0.5
Ω 2 Ω 1 Ω
V
s
r
R
V
l
Figure 5.1 Peltier device connected
to a load resistor