Re: experimental latent heat of evaporation

[Ludwik Kowalski <kowalskil@MAIL.MONTCLAIR.EDU>]

On Monday, Sep 27, 2004, at 23:20 America/New_York, Ludwik Kowalski
wrote:

> Prompted by good comments I went to the school laboratory this
> afternoon and attempted to measure L. Unfortunately, my results
> fluctuated widely and I have no idea why. The average result from 8
> attempts was 1344 J/gram (instead of 2260); the smallest value was 800
> and the largest was 3030. The method I "invented" is straight forward;
> it has probably been used by others. Expecting critical comments I will
> post a short description of the method tomorrow. Perhaps those who are
> familiar with thermal measurements will help me.
> Ludwik Kowalski

Well, I did not wait till tomorrow. Here is my piece.

A 600 cc beaker (mass = 182.5 grams) is filled with 400 grams of water.
Then it was placed on a wooden tile supported by a scale. That scale
was used to determine the amount of water, m (typically 10 grams),
evaporated during a specified time t (typically 10 minutes). A resistor
of 40 ohms, connected to a d.c. power supply, was immersed into water.
The heating power was determined from the measuring current and
voltage. The experiment started when water in the beaker (always close
to 400 grams) reached a constant temperature. It consisted of measuring
m and t. I assume that the constant temperature implies

electric energy supplied = thermal energy lost.

In other words,

V*I*t = Qe + Qc = m*L + Qc                   (1)

where Qe is the energy needed to evaporate m grams of water and Qc is
the energy lost in time t due to conduction, convection and radiation.
The value of Qc depends on the constant temperature, for example 100 C
or 70 C, on the geometry of the setup and on the  known heat capacity
(m1 grams of  water and m2 grams of glass). More specifically,

Qc=(c1*m1 + c2*m2)*R*(t/60)               (2)

where c1 and c2 are specific heats of water and glass and R is the
experimentally measured cooling rate at the chosen constant
temperature. Division by 60 was necessary because values of R were in
degrees per minute (t is in seconds). At the boiling temperature, for
example, R=3.5 degr/min, while at 80 C it is 2 degr/ min. These values
were obtained from the cooling curve (temperature versus time). One
cooling curve was taken before the the experiment and another was taken
after the last experiment. The two curves were practically identical.
The heat of evaporation was calculated as

L =( V*I*t - Qc)/m                                       (3)

That is it. I am certain that V*I*t values do not fluctuate by more
than 5%. Likewise, the error in m is most likely smaller than 5%. Thus,
if there were no errors in Qc then the values of L should be
reproducible within 10% (most likely to within 5%). But my values of L
fluctuate more widely. I suspect that this has something to do with R.
I see nothing wrong with my method of determining R; two cooling curves
were practically identical. Is my method of finding L acceptable? Do
you see something wrong in its use?

At the beginning I said that eight attempts to find L were made. What I
did not say was that each attempt was made at a different heating rate
(some with bubbling and some without bubbling). I did not expect
troubles and I wanted to see if L depends on the rate of bubbling. I
see no consistent pattern in the results. I suspect that the values of
L would fluctuate even if the temperature was the same in all eight
experiments. Please help.
Ludwik Kowalski