Re: is it better to use a dry ice bath or liquid n2 for freeze drying?

Dear Derrick:

Thanks for your interesting question. Were we should start?. I think it will be useful to give some definitions and background:

In the Encyclopedia Britannica we can read that latent heat is the characteristic amount of energy absorbed or released by a substance during a change in its physical state that occurs without changing its temperature. The latent heat associated with melting a solid or freezing a liquid is called the heat of fusion; that associated with vaporizing a liquid or a solid or condensing a vapor is called the heat of vaporization.

For example, when a pot of water is kept boiling, the temperature remains at 100º C (212º F) until the last drop evaporates, because all the heat being added to the liquid is absorbed as latent heat of vaporization and carried away by the escaping vapor molecules. Similarly, while ice melts it remains at 0º C (32º F), and the liquid water that is formed with the latent heat of fusion is also at 0º C.

The structure of a crystalline solid is maintained by forces of attraction between the individual molecules or ions, which oscillate slightly about their mean positions in the array. When heat is absorbed, these motions increase until at the melting point the attractive forces can no longer preserve the orderly arrangement, and the solid changes into a liquid, in which the individual particles move about independently, attracted to each other only by forces much weaker and less specifically directed in space. When a substance is heated sufficiently, even the weak forces that hold the particles together in the liquid state are overcome, and at the boiling point the liquid transforms into vapor.

Latent heat is associated with processes other than changes between solid, liquid, and vapor phases of a single substance. Many solids exist in different crystalline modifications, and the transitions between these are generally attended by absorption or evolution of latent heat. The process of dissolving one substance in another often involves heat; if the solution process is a strictly physical change, the heat is a latent heat. Sometimes, however, the process is accompanied by a chemical change, and part of the heat is that associated with the chemical reaction.

Now, at www.treasure-troves.com (latent heat) we find that for water, the latent heat of vaporization is 540 cal g-1 In this site we are also told that the heat capacity C of a substance is the amount of heat required changing its temperature by a given amount, and has units of energy per degree. The heat capacity is therefore an extensive variable since a large quantity of matter will have a proportionally large heat capacity. A more useful quantity is the specific heat (also called specific heat capacity), which is the amount of heat required to change a given quantity of a substance by a give temperature. This is an intensive variable and has units of energy per mass per degree.

It is important to bear in mind that the specific heat capacity of a substance depends on its molecular structure and on its phase (see http://www.sasked.gov.sk.ca/docs/physics/u4b2phy.html)

Lets look for some numbers. In http://www.trgn.com/database/cryogen.html we find that the latent heat of vaporization of nitrogen is 198.3 kJ/kg @ 1 Atm or (see http://www.noao.edu/ets/gnirs/SDN0007-02.htm) 1.61 x 10^5 J/l).

Moreover, the specific heat capacity for nitrogen is 1.006 J/g K according to the following site on conversion factors.

Probably you could be interested in checking this information were a careful experiment for measuring the heat of vaporization of nitrogen is outlined

For ethanol we find that the latent heat of vaporization = 9674 cal/g mole (although another commonly used value is 9.22 kcal/mol @ 351.7 K), and according to this reference its specific heat capacity is 2.438 J/g K

Since both, the latent heat of vaporization and the specific heat capacity, are bigger for ethanol than for nitrogen (198.3 kJ/kg = 1.3268 kcal/mol) ethanol seems to be a better refrigerant.

Remember that all those values correspond to the liquid phase. If the liquid evaporates on a given surface, it will cool down that surface. This is because the liquid will extract an amount of heat equal to its latent heat of vaporization.

If only the vapor is used for the cooling an object, the final temperature of the object will be, ideally, equal to the (constant) vapor temperature.

If we are interested in how fast the cooling is performed, we could use the method outlined in Netwon's Laws of Cooling which provides:

t2 = t1(ln((T0-Ts)/(T2-Ts))/ln((T0-Ts)/(T1-Ts)))

This equation tell us at what time (t2) the system will reach temperature (T2) provided that we know which is the temperature (T0) at (t0), the temperature (T1) at (t1) and the temperature of the heat source (Ts)

In a related subject, it is worth mentioning that the basic components of a modern vapor-compression refrigeration system are a compressor; a condenser; an expansion device which can be a valve, a capillary tube, an engine, or a turbine; and an evaporator (see the excellent entry in Encyclopedia Brittanica).

The gas coolant is first compressed, usually by a piston, and then pushed through a tube into the condenser. In the condenser, the winding tube containing the vapor is passed through either circulating air or a bath of water, which removes some of the heat energy of the compressed gas. The cooled vapor is passed through an expansion valve to an area of much lower pressure; as the vapor expands, it draws the energy of its expansion from its surroundings or the medium in contact with it. Evaporators may directly cool a space by letting the vapor come into contact with the area to be chilled, or they may act indirectly--i.e., by cooling a secondary medium such as water. In most domestic refrigerators, the coil containing the evaporator directly contacts the air in the food compartment. At the end of the process, the hot gas is drawn toward the compressor.

It will also be interesting for you to learn about heat pipes (second reference.)

Finally, you can learn how a commercial device is designed to use liquid nitrogen as a refrigerant and yet avoid the complications of a vigorous boiling. It reads in part:

"Liquid nitrogen flows from the reservoir through the adjustable flow valve to the vaporizer at the bottom of the sample tube. Applying heat vaporizes the liquid and raises the gas temperature. This gas enters the sample zone to cool the sample to your selected temperature. Load your samples into this flowing nitrogen gas that exits from the vaporizer, (also known as the diffuser or heat exchanger). Samples can be changed while operating. The central sample tube is surrounded by the liquid nitrogen reservoir. Load your samples into this tube; adjust the amount of exchange gas and samples will immediately begin to cool. The exchange gas thermally couples the sample to liquid nitrogen. The amount of thermal coupling depends on the exchange gas pressure."

I hope this helps.

Regards

Jaime Valencia