In another experiment, you place a layer of this cryoprotectant between one 10 cm × 10 cm cold plate maintained at -40°C and a second cold plate of the same size maintained at liquid nitrogen’s boiling temperature (77 K). Then you measure the rate of heat transfer. Another lab wants to repeat the experiment but uses cold plates that are 20 cm × 20 cm, with one at -40°C and the other at 77 K. How thick does the layer of cryoprotectant have to be so that the rate of heat transfer by conduction is the same as that when you use the smaller plates?

(a) One-quarter the thickness;

(b) Half the thickness;

(c) Twice the thickness;

(d) Four times the thickness.

In cryopreservation, biological materials are cooled to a very low temperature to slow down chemical reactions that might damage the cells or tissues. It is important to prevent the materials from forming ice crystals during freezing. One method for preventing ice formation is to place the material in a protective solution called a cryoprotectant. Stated values of the thermal properties of one cryoprotectant are listed here:

Melting point .......................................................... -20‑C

Latent heat of fusion .............................................. 2.80 × 10⁵ J/kg

Specific heat (liquid) ............................................... 4.5 × 10³ J/kg ∙ K

Specific heat (solid) ................................................. 2.0 × 10³ J/kg ∙ K

Thermal conductivity (liquid) .................................... 1.2 W/m ∙ K

Thermal conductivity (solid) ..................................... 2.5 W/m ∙ K