Physics Department
Thermodynamic Laboratory
Vaporization Heat of Liquid N2
1. Goal

Determination of the latent heat of vaporization of liquid Nitrogen.
2. Foundations
Warning: Liquid nitrogen can cause terrible burns (death of living
tissue caused by the extreme cold).
Latent heat, l , is the heat released or absorbed by a chemical substance or a
thermodynamic system during a change of state that occurs without a change in
temperature. The more common forms of latent heat are latent heat of fusion (melting)
and latent heat of vaporization (boiling).

We will start pouring liquid nitrogen on a polystyrene vessel. Liquid nitrogen is colorless
and odorless and its boiling temperature is 77ºK. Since at room temperature (25ºC or
298ºK) we are well above the boiling temperature, liquid nitrogen will be evaporating, Fig. 1.
Figure 1
Liquid nitrogen gets heat from its environment, i.e. container and atmosphere, and uses it
for a phase transition from liquid to gas. Since, by definition, the latent heat of vaporization
is the amount of heat necessary to evaporate a unit mass, the heat exchanged with the
surroundings per unit time,  A , can be used to evaporate dm dt 0



A  l
dm 
 dt 0

[1]

1
To determinate the latent heat of vaporization, l , we will measure the lost mass rate,
dm/dt, using an analytical bascule and a chronograph. But, how to measure  A ? The answer
is: introducing an additional known heat source. The one that will be used is based on the
Joule effect, the heat delivered per unit time by an electrical resistance  E  IV .


The two heat sources: the environment, contributing with  A , and the electrical
resistance  E , will be used together to evaporate the liquid nitrogen:

A  B  l


where dm dt
dm 
 dt I
 [2]
1 is the amount liquid nitrogen evaporated per time unit. Combining equations
[1] and [2] and the
 Joule effect:

l
dm 
dm 
 IV  l
 dt 0
 dt I
[3]
thus giving the following expression for the latent heat of vaporization:

l 
IV
dm  dm 

 dt I  dt 0
[4]
3. Learn more ...

 Paul A. Tipler, Gene Mosca “Physics for Scientists and Engineers”, Vol. 1, 6th Edition.
Ed. W. H. Freeman; ISBN-10: 0716789647, ISBN-13: 978-0716789642 (2007)
4. Equipment
1. Polystyrene vessel.
2. Analytical balance.
3. Electrical resistance.
4. Chronograph.
5. Voltmeter and ammeter
6. Regulated power supply.
7. Liquid nitrogen.
2
Figure 2
5. Experimental setup.
5.1 Description of the measurement system.
Place the polystyrene vessel on the analytical balance and fill it with liquid nitrogen. Make
the electrical connections according to Fig. 3. Don’t turn on the power supply yet. Insert
the electrical resistance in the nitrogen. We will assume that the current, I , and potential
difference, V , will be those indicated by the power supply.


Figure 3.
3
5.2 Measurements.
To estimate the latent heat of vaporization with equation [4] we need to measure: i) the
evaporation rate of nitrogen without connecting the electrical circuit v 0  dm dt 0 , ii) the


current flowing in the resistance I , iii) the potential difference V , and finally, iv) the
evaporation rate of nitrogen with the electrical circuit on, v I  dm dt I . Since the heat


exchange with the surroundings changes with time several estimations of it are needed.



5.2.1 First measurement of V0. Fill the 5.2.1 part of the form
 Setup the equipment according to Fig. 3. Don’t
connect the power supply yet.
 For the next 4 minutes, record the nitrogen-vessel set weight m(t) every 20 seconds.
 Calculate how much nitrogen has evaporated mv  m(t)  m(t  0) .
 Plot m v vs. t .


Calculate the slope and y-intercept of a straight line least squares fit to your data.

Estimate v 0  dm dt 0 from the least squares fit parameters.





5.2.2 First measurement of VI. Fill the 5.2.2 part of the form







Turn on the power supply and adjust the current intensity to 2 A.
Record the current intensity and the potential difference.

For the next 4 minutes, record the nitrogen-vessel set weight m(t) every 20 seconds.
Calculate how much nitrogen has evaporated mv  m(t)  m(t  0) .
Plot mv vs. t .
Calculate the slope and y-intercept of a straight line least squares fit to your data.

Estimate v I 2  dm dt I 2 from the least squares fit parameters





5.2.3 Second measurement of V0. Fill the 5.2.3 part of the form






Turn off the power supply.
For the next 4 minutes, record the nitrogen-vessel set weight m(t) every 20 seconds.

Calculate how much nitrogen has evaporated mv  m(t)  m(t  0) .
Plot mv vs. t .
Calculate the slope and y-intercept of a straight line least squares fit to your data.

Estimate v 0  dm dt 0 from the least squares fit parameters





5.2.4 Second measurement of VI. Fill the 5.2.4 part of the form







Turn on the power supply and adjust the current intensity to 3 A.
Record the current intensity and the potential difference.

For the next 4 minutes, record the nitrogen-vessel set weight m(t) every 20 seconds.
Calculate how much nitrogen has evaporated mv  m(t)  m(t  0) .
Plot mv vs. t .
Calculate the slope and y-intercept of a straight line least squares fit to your data.

Estimate v I 3  dm dt I 3 from the least squares fit parameters





5.2.5 Third measurement of V0. Fill the 5.2.5 part of the form







Turn off the power supply.
For the next 4 minutes, record the nitrogen-vessel set weight m(t) every 20 seconds.

Calculate how much nitrogen has evaporated mv  m(t)  m(t  0) .
Plot mv vs. t .
Calculate the slope and y-intercept of a straight line least squares fit to your data.

Estimate v 0  dm dt 0 from the least squares fit parameters.





4
5.3 The latent heat of vaporization of liquid Nitrogen
We will obtain two estimates of the latent heat of vaporization of liquid nitrogen, one for
I  2 A and the other for I  3 A.

5.3.1 I = 2 A.
 Estimate the evaporation rate, v 0 , of liquid nitrogen with I  0 A averaging the
results of
sections 5.2.1 and 5.2.3.
 Estimate the latent heat of vaporization l I 2 inserting the values of the evaporation
rate v 0 , the evaporation rate v I 2 (5.2.2), the current intensity and potential


difference in equation [4].

5.3.2 I = 3A.

Estimate
the
evaporation
rate,
v 0 , of liquid nitrogen with I  0 A averaging the


results of sections 5.2.3 and 5.2.5.
 Estimate the latent heat of vaporization l I 3 inserting the values of the evaporation
rate v 0 , the evaporation rate v I 3 (5.2.4), the current intensity and potential


difference in equation [4].

5.3.3 Compare results.
 Compare and discuss the

results obtained in the previous two sections for the latent
heat of vaporization of nitrogen.
5