Experiments in Thermodynamics

							1999.

Introduction:

	The purpose of these experiments is to demonstrate the law of
conservation of energy and how thermal energy acts in accordance with this
law.  Thermal energy is defined as the sum of all the kinetic and
potential energy of a body.  A body has kinetic energy on the atomic level
because atoms vibrate within the body.  The potential energy of the body
is caused by the atoms change in position from the kinetic energy. Change
in thermal energy of a body can be found using the equation (if the change
in energy does not cause a change in state (solid, liquid, gas)):  "Change
in thermal energy = (mass of body)(specific heat of substance)(change in
average kinetic energy in kelvins)" or "Q = mC(Tf-Ti)."  Average kinetic
energy of a body is also known as the body's temperature, since the
measure is per particle, temperature is not affected by mass.  The
specific heat of a substance is the amount of thermal energy required to
increase the temperature of one unit substance, usually kilograms, one
unit temperature, usually kelvins or degrees Celsius. 
  If the amount of thermal energy causes the substance to change state,
the entire body remains at the same temperature until the entire substance
changes state.  Since there is no change in temperature, the formula
Q=mC(Tf-Ti) would yield 0, which is not correct, instead to calculate the
energy required for a phase change you must use the formula "Change in
thermal energy = (mass of body)(heat of fusion or vaporization)" or "Q =
mHf."  Heat of fusion is the amount of energy required to change one unit
mass from solid to liquid (heat of vaporization, Hv, from liquid to gas).
  In a two-body system, since energy is conserved, the energy lost (or
negatively gained) by one substance equals the energy gained by the other,
so that QsubA = -QsubB.  Each of the three experiments proves a different
aspect of the change in heat acts in compliance with the law of
conservation of energy. 
  The first experiment, labeled 19, showed that thermal energy lost to
another body with no phase changes conserved energy.  The energy lost from
the hot water as it transfered energy from a warmer body (one with a
higher average kinetic energy) to a cooler body (one with a lower average
kinetic energy) are equal to each other.  It also demonstrated the first
law of thermodynamics, thermal energy is always transfered from a warmer
body to a cooler one.
  The second experiment, labeled 20, the law of conservation of energy
that was demonstrated in experiment one is used to identify the specific
heat of an unknown metal and ultimately identify the metal. 
  The final experiment, labeled 21, energy from water was conserved when
transfered to the ice and used in changing it to another state.  Ice
underwent a phase change using energy, and raise the temperature once the
ice melted. 


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Discussion:

	From the results of these experiments, it can be concluded that
thermal energy follows the law of conservation of energy.  Energy lost by
one body equals energy gained by other bodies in a system. 
  In the first experiment, the calculations for the amount of energy
gained by the cold water and calorimeter cup differed from the amount of
energy lost by the hot water by a value of only 1.4x10^3 J.  To put that
value into perspective, that amount of energy would change the temperature
of 111.07g, the amount of warm water, by about 3 degrees Celsius. This
error can be attributed to energy that was lost to the surrounding air
while the temperature of the warm water was being measured, before being
placed in the calorimeter. 
  The second experiment had an unknown metal, later to be identified, that
based on the amount of energy it lost per unit mass, the specific heat was
calculated.  The nearest metal with similar properties and a similar
specific heat was lead, with a specific heat of 0.130 J/g-C.  From these
results, we were able to determine that our measurements were inaccurate
by 10%, favoring a metal with a lower specific heat.  Based on the data
observed and the calculations, this could have also been due to cooling
while in transit to the calorimeter, having decreased in temperature by
7.2 degrees Celsius.  The metal losses energy faster to air due to it's
lower specific heat.  But it should also be noted that the two trials
whose data was averaged with each other were measured from two different,
but similar, metal samples. 
  The goal of the third experiment was to calculate the heat of fusion for
ice based on how much energy was unaccounted for in the calculation for
the amount of energy the ice used once converted to water.  When the
experiment was performed, a 61-percent error was the result.  The amount
of energy that appears to have disappeared is sufficient to convert 20.0g
of ice to water.  This enormous error is due to many factors, such as
averaging the data for the trials, the data is too varied to allow for
averaging of trials.  Other sources of error include the ice not being
zero degrees as recorded due to atmospheric conditions. 

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Conclusion: 

	These experiments supported the law of conservation of energy, and
the second law of thermodynamics.  The law of conservation of energy was
supported when a low amount of error in the first experiment showed that
energy lost by one body is the same as the heat gained by other bodies.
The second law of thermodynamics was supported by all three experiments,
energy always went from the body with a higher temperature to the bodies
with lower temperatures.