A. L. Dmitriev, E. M. Nikushchenko, N. N. Chesnokov
St. Petersburg National Research University of Information Technologies, Mechanics and Optics,
49 Kronverksky Prospect, St-Petersburg, 197101, Russia
Abstract. Weight (mass) of airtight container about 1.1
with electromechanical vibrator built-in inside, with independent supply and contactless control, has been measured. Decrease of container mass up to 170
, basically, is determined by heating of copper wire of vibrator electromagnet and practically is not related to artifacts – change of buoyancy, air convection, electromagnetic interference.
PACS: 06.30. Dr
Problems referring
to the influence of accelerated motion and body temperature on its physical
weight (gravity mass) have been repeatedly discussed [1-6]. The results concerning
weighing of mechanical rotor with horizontal axis of rotation and indicative of
dependence of rotor mass being measured on its angular velocity of rotation are
given in [3].The results of experiments concerning precise weighing of
insulated containers with sample of metal being heated electrically or
chemically are described in [7]. Data of these measurements demonstrate relatively
strong negative temperature dependence of mass of nonmagnetic metals (brass,
titanium, copper etc.) with relative value 
about 
. In the given experiment weighing of massive
cylinder container with electromechanical vibrator installed inside with mild
steel core oscillating along the vertical has been carried out. Structure of
container is given in Fig. 1.
Fig. 1. Structure of container. 1,2 – hermetically connected parts of housing; 3 – batteries; 4 – electromechanical vibrator (contains electromagnet and core supported by springs); 5 – heat seal; 6 – pulse generator; 7 – photodiode generator control.
Parts and details
of container were tightly connected and junction points were filled with bi-component
polymer adhesive providing almost complete tightness of entire construction. Mass
of assembled container - 1104.346 g, batteries - 213 g, vibrator core - 2.36 g. Switching on/off of unipolar pulse generator with amplitude 12 V, duration
of 2.9 ms and period of 4.4 ms was carried out by visual signal setting to
photodiode 7. Container was weighted using Manual Mass Comparator ССЕ 1005 (“Sartorius AG”) in special metrological room at air
temperature 21.8
,
relative humidity 36% and atmospheric pressure 1017 hPa. Error (discreteness) of
mass counting didn’t exceed the value of 10 . Contactless control of the pulse generator
connected to vibrator was carried out via glass wall of balance showcase (ordinary
laser pointer was used).
An example of typical time dependence of container mass change is given in Fig. 2.
Fig. 2. Time dependence of container mass change
Pulse generator was switched on at time «1» and switched off within 20 sec at time «2»; the readouts of the balance were carried out every 20 sec. The effective value of the amperage within exciting coil was 500 mA.
The internal
resistance of the battery is significantly lower than the resistance of the vibrator
electric coil with value of 12 
, and power loss within the battery as
well as within generator circuitry is also much less than on load resistance.
Therefore, the heat is being released basically within vibrator electric coil. In
this case relatively slow propagation of the heat wave within coil copper wire and
as a result of heat exchange within housing of vibrator coil and insulating
layers is observed.
Energy 
, dissipated in resistance
of vibrator
winding is equal 
,
where 
- effective
current, 
and 
sec – current
duration. Design value , equal to 60 J, allows to evaluate the order
of 
change
of temperature of copper wire, 
, where 
g – mass of wire and 
- specific heat
capacity of copper, therewith 
. Actual value of is about half as much due to heat
exchange processes given above. This fact is proved by time dependence (shown
in Fig. 3) of surface temperature of vibrator electric coil by passing of direct
current with value 500 mA equal to effective current by weighing; the given
dependence is measured in adiabatic regime of heating when the thermosensor and
coil have been thoroughly thermally insulated. It can be seen that increase of
coil surface temperature within first 3 minutes of measurements didn’t exceed 
.
Fig. 3. Surface temperature of thermally insulated coil of vibrator electromagnet by direct current 500 mA (heating time 20 sec, start heating at time «1», one marking of time scale 15 sec)
Fig. 4. Time dependence of container lid temperature (one marking of time scale 30 sec).
Fig. 4 gives time
dependence of temperature of container upper lid obtained at the same switching
on regime of vibrator as by weighing. It follows from the figure that within
first 80-100 sec of observations in which the change of container mass achieves
maximum value of about 170, the temperature of container lid
monotonically increases not more than by 
. Thereby, as it can be shown using Glaser
theory [8], the apparent decrease of container mass determined by air
convection doesn’t exceed 12. Insignificant influence of convection on
measurement results is proved as well by the common time course of container mass
dependence shown in Fig. 2 and its comparison with Fig. 4.
The reason of container weight (mass) change is obviously of thermal nature, i. e. it is related to heating and further, within 1-1.5 minutes after start measurements, slow cooling of vibrator coil, as well as to lesser extent it is related to heating of power supplies and electronic devices of signal generators. Deformation of massive steel container housing caused by insignificant change of air pressure within its volume is practically equal to zero, therefore, change of buoyancy (Archimedes force) affecting the results of weighing is also equal to zero. The extreme nature of time dependence of the container mass change considering monotonic, over the period of more than 5 minutes, dependence of the container lid temperature (Fig. 4) indicates that fundamentally possible insignificant depressurization of the container (leakage) doesn’t cause the decrease of mass being observed. The fact that decrease of the container mass occurs within one minute after vibrator switching off confirms that electromagnetic and vibrating (acoustic) interference couldn’t cause the observed time dependence of the mass value. Referring to Fig. 2, the container gross mass slowly returns to its initial value as a result of heat dissipation within container, heat transfer from its surface and decrease of temperature of vibrator coil.
Let’s
calculate relative temperature weight change of the vibrator coil copper wire 
, where 
, therewith 
(
, 
,). Sign and order of the given magnitude
are well agreed
with values obtained in [4-6].
So, the experimental results displayed in the given article confirm previously noticed relatively strong negative temperature dependence of the copper specimen physical weight. It is expedient to fulfill further experimental studies using precision scales in vacuum to explain the dependence being observed.
The authors express their gratitude to V. A. Korablev for consultation with regard to temperature measurement technique.
