Download Manual(Exp.1)

Physics Laboratory 2
last update: 2009. 8. 31
Exp. 1. Form of Energy
- Conservation of Thermodynamic Energy -
Purpose of Experiment
Energy of a system can be changed by the heat transfer in addition to mechanical ways.
In other words, the heat is a way of energy transfer. For the system exchanging heat
with its surroundings, the change of the internal energy by the heat and that by the
mechanical ways give the same result although they passed different courses. It
corresponds to the transfer of water in a dam, in which the amount of water is changed
not only by the in-and-out process on the gate but also by the rain or evaporation. But
the water from different sources can't be distinguished.
Since the heat and the work have been using different units even though they represent
the same physical quantity (energy), we need the conversion factor for their quantitative
comparison. This factor is called the mechanical equivalent of heat, which is firstly
measured by James P. Joule as 1 cal (calorie) is equivalent to 4.2 J (joules) (more
exactly, 4.1860 J)
In the system where the internal energy can be changed by the heat and the work, its
mechanical energy might not be conserved. It could be emitted in the form of heat, or
the influx of heat could make the system work. Even in the internal system alone, there
could be the energy exchanges between heat and work. However, if the system is
isolated from the external system, the total of the heat and mechanical energy is not
varied. This is called the conservation of heat and mechanical energy (conservation of
total energy), and the mechanical energy conservation exists only in the system where
there is no energy variation by the heat.
In this experiment, we measure the internal energy changes, understand the way to vary
the internal energy, measure the mechanical equivalent of heat and measure the specific
heat of an object.
- From Halliday & Resnick, Fundamentals of Physics
To melt the ice in the picture, the energy to launch the same ice to 34m high or the work to
accelerate the same ice to 93 km/h is required.
Outline of Experiment

Understand the essences of the heat and internal energy.

Measure the change of internal energy by the influx of heat using a calorimeter.

Calculate the heat capacity of the calorimeter and the specific heat of an object (plumb).
Experimental Method
These equipments are prepared in the laboratory. (Parentheses mean the number of
them.)
calorimeter (1)
digital thermometer (1)
DC constant current(voltage) power supply (1)
heating wire (1)
stirring stick (1)
mass cylinder (1)
object (50g plumb) (1)
electric wire with crocodile clip (2)
clothespin (1)
stopwatch (prepare individually)
toilet paper (prepare individually)
If you need more stuff, inquire to your teaching assistant or experiment preparation
room (19-114), or prepare yourself. And you should learn in advance about usages of
DC constant current(voltage) power supply and calorimeter and about how to measure
the temperature using digital thermometer and thermocouple.
The following is a recommended experiment method.
Experimental Setup (video link)
1) Measure the amount of water using mass cylinder, then pour it into the calorimeter.
① Check the inner wall of calorimeter for wetness. If it is wet, clean using toilet
paper because it could affect the experiment.
② Let the amount of water be 100 cc.
③ Pour the water into the calorimeter. Then put the thermocouple of digital
thermometer into the hole at the center of the calorimeter. Note that the end of
the thermocouple must not touch bottom, wall and heating wire. Float it 1 cm
above the bottom.
[comment 1 : Clip the thermocouple using the clip, and lay it on the lid of
calorimeter.]
[comment 2 : When using the digital thermometer, only use T1 and insert it with
wide side down.]
④ Move up and down the stirring stick until the temperature of water doesn't
continuously increase or decrease.
2) Applying constant current, measure the temperature change of water.
① Connect two connectors of the heating wire to (+) and (-) output connectors of
the power supply.
② Confirm the voltage control handle and the current control handle are at 0.
Then turn on the power.
③ Set the voltage control to 8V, and push CC/CV button to light CC indicator.
④ Use the current control buttons (up or down) to set the current to 2A.
[comment 1 : If the current is not changed, check electric wires are connected
well. If it isn't or the voltage exceeds 30V because of too high resistance, you
cannot get desired current.]
[comment 2 : If the temperature doesn't increase well, raise the current to
about 3A. The new power supply can be raised up to 5A.]
Record the output current and voltage.
⑤ Record the temperature at regular time intervals (5~10 secs)
[comment 1 : Adjust the time interval depending on the speed of changing
temperature.]
[comment 2 : Confirm that the mechanical energy applied by this stirring
action doesn't affect the measurement.]
[caution : As the temperature increases, heating wire's resistance could be
changed, then the voltage will be changed to flow a constant current. Thus
record the change of the voltage with respect to the time.]
⑥ Continue this measurement about 5 minutes or until the water's
temperature goes up to 5˚C.
[comment : If the temperature doesn't change more than 5˚C after 5 minutes,
increase the current.]
⑦ Record the temperature over time like below.
[comment : It is convenient for data analysis to use Excel or Notepad using
computer.]
Every time you measure, check the voltage and record if it is changed.
Time[s]
Temperature[degree C]
1
19.69
5
19.71
10
19.69
15
19.71
20
19.73
25
19.69
30
19.72
35
19.71
(ellipsis)
300
23.58
310
23.63
320
23.71
330
23.79
340
24.05
For the experiment report, you can use data analysis software such as Excel or
graphing software such as Origin.
[caution : treat significant figures carefully when displaying fitting lines.]
3) Using 4 different amounts (e.g. 120, 140, 160, 180 cc) of water, repeat 2) so that
measure the heat capacity of the calorimeter and the mechanical equivalent of heat. Use
fresh water for each measurement, and adjust the measurement time properly according
to the amounts. [comment : The heat capacity of a calorimeter can be attained by
measurement of the specific heat.] [caution : Turn off the power supply before cutting
the electric wires from the heating wire.]
4) After the last measurement ends, turn off the power supply and measure the
decreasing of water's temperature over time until it lowers more than 1˚C. And then
calculate the heat loss rate of the calorimeter.
5) If time allows, put the prepared object (plumb 50g) in calorimeter with 100cc of
water, repeat 2). By comparing it with the result of 2), calculate the specific heat of the
object.
6) Turn off digital thermometer, power supply, computer and monitor. And pull out the
plug.
You could write the experiment note like ⑦ of 2). Especially, for the case in which the
voltage is changed as the temperature changes, It is better to graph the temperature with
respect to the applied energy (total amount of heat) than simply to the time.
(Measurements of the temperature change of water by a heating wire over time)
current of heating wire I =
voltage of heating wire V =
A
V
---------------------------------------
mass of water m =
kg
---------------------------------------
Time t(min) Voltage V(V) Power P(W)
Total Energy E(J)
Temperature T(˚C)
--------------------------------------------------------------------------------------
--------------------------------------------------------------------------------------
slope : dE/dT =
J/K ±
J/K (=
cal/˚C ±
cal/˚C)
------------------------------------------------------------------------
Background Theory
For the system exchanging heat and work with its surroundings, the internal energy change dU is
given by
where dQ is the thermal energy absorbed by the system and dW is the work done by the system.
When there is no energy inflow (dQ=0, dW=0) such as in an isolated system, the internal energy
of the system remains constant (dU=0). This is called as the principle of conservation of
mechanical energy.
When current flows by applying voltage V to a resistor (the heating wire of calorimeter), heat is
generated at a rate
.
We call it the Joule heat. The temperature increased by this heat corresponds to
where m(kg) is the mass of water, c(cal/kg·K) the specific heat and q is the mechanical
equivalent of heat. One calorie is defined as the amount of thermal energy required to raise the
temperature of 1g of water from 14.5˚C to 15.5˚C. The specific heat is the thermal energy per
unit mass required to raise the temperature by unit temperature, thus water's specific heat is c = 1
cal/g·K or 4190 J/kg·K [In this case, q=1]. The heat capacity of an object is (specific heat ×
mass).
As the temperature of water is increased, so does the temperature of calorimeter itself. Some part
of the heat is absorbed into the calorimeter so that it increases the internal energy of calorimeter
itself. Therefore the heat generated by a heating wire increases the temperature of water by the
rate of
where C(cal/K) is the specific heat of calorimeter including a heating wire and a thermometer,
and m(kg) is the mass in calorimeter. By measuring the temperature increasing rates dT/dt for
several different amounts of water, we can draw a graph where (dT/dt)-1 is the vertical axis and
m is the horizontal axis, which shows a straight line in agreement with equation (4). Its slope is
103 q/P and it meets the vertical axis (m=0) at qC/P. Hence we can obtain the values of the
mechanical equivalent of heat c and the heat capacity of calorimeter C.
Although the calorimeter was designed for minimizing the heat transfer, it's not perfect. This can
be shown by measuring the temperature of water with respect to the time after disconnecting the
current from the heating wire. The main contributors are the heat escape to the surface of
calorimeter and the transfer and radiation to the outside air and the transfer from the
thermocouple. We must consider these losses for precise analysis. The heat loss rate can be
obtained from the temperature decreasing rate dT'/dt measured at the last part as
Inserting this into P of equation (4), which can be written by
But note we have assumed the heat loss rate P' and the heat capacity of calorimeter are
independent on the mass of water m. Ponder on its validity and conclude from the results of
experiment.
Now, when an object of the specific heat c'(cal/kg·K) and mass M(kg) is heated with water of
mass m(kg), the temperature increasing rate is
,
we can calculate the specific heat c' of the object by the difference of temperature change rate
from the equations (6) and (7).
References

Constant current(voltage) power supply

Measurement of specific heat of an object - calorimeter

Measurement of temperature by the thermocouple and the digital thermometer

Treatment of measurement data

Analysis method based on the graph

James Joule - The importance of precise measurement
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