# Physics 120/130

## Latent Heat of Vaporization of Liquid Nitrogen

## I. __Introduction__

Liquid
Nitrogen boils (liquid --> gas) at 77 Kelvin. At room temperature, Nitrogen
naturally boils quite rapidly, as 293 Kelvin is well above its boiling point. In
this lab, we will measure the amount of thermal energy that it takes to change
nitrogen from its liquid to its gaseous state (the latent heat of vaporization)
by measuring how much liquid Nitrogen is boiled off in order to cool some lead
shot from room temperature to 77 K.

If we know the specific heat of lead, we can find out how much energy
the lead must emit to cool from room temperature to 77 K: since the specific
heat is the heat capacity per unit mass, then the specific heat, *c*,
is

,

where m is the mass of the lead Q is the amount of heat absorbed by the
liquid nitrogen from the lead, and DT is the temperature change of the lead.
Now we know how much energy is added to the liquid nitrogen, and we can
calculate its latent heat by measuring the mass of evaporated nitrogen since the
latent heat is just the heat absorbed per unit mass.

We should note that we must be careful when we talk about the specific
heat of lead. Unlike it is treated
in class, it is found that the specific heat of a substance is not constant over
a large temperature range (from 77 K to 293 K, for example).
We must be careful, therefore, when we talk about *the*
specific heat of a substance. The
specific heat of lead varies as a function of temperature from approximately
5.68 cal/mole K at 77 K to approximately 6.37 cal/mole K at 300 K.
The average value of the specific heat between these two temperatures is
found to be about 6.12 cal/mole-K. **(***Be
sure you are using the correct units when you use this specific heat in a
calculation.*)