Careful measurements show that the specific heat of the solid phase depends on temperature (Fig. P17.117). How will the actual time needed for this cryoprotectant to come to equilibrium with the cold plate compare with the time predicted by using the values in the table? Assume that all values other than the specific heat (solid) are correct. The actual time

(a) Will be shorter;

(b) Will be longer;

(c) Will be the same;

(d) Depends on the density of the cryoprotectant.

Figure P17.117

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 ˆ™ K

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

Thermal conductivity (liquid) .................................... 1.2 W/m ˆ™ K

Thermal conductivity (solid) ..................................... 2.5 W/m ˆ™ K

Transcribed Image Text:

c (J/kg - K) 5000 4000 3000 2000 1000 T("C) 50 200 –150 –100 -50 0