# Advanced Heat transfer I - Heat conduction by hwlsj1R9

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```									                           ME 8381 Bioheat and Mass Transfer
Spring 2010 - Bischof

Homework #1           - Due date TBA

1. Obtain a copy of the Mathematic Tutorial from the website and begin to play with
solutions.

2. What is the amount of work necessary to move 1 mole of K+ ions against the normal 70
millivolt potential across cell membrane.

3. (Will give hint). Using the standard expression for chemical potential: ∆µ = RT
ln[nw/(ns + nw)] please show how at osmotic equilibrium osmotic pressure (i.e. an
effective rise due to pressure) can be achieved by addition of a number of moles of solute
ns . Use this to derive the usual expression for osmotic pressure π = RT m, where m is
molarity (ns/V).

4. Using the Clauisius Clapeyron equation show that a drop of –0.0075 °C occurs in the
phase change temperature of water for every atmosphere of pressure. How much
pressure would a 70 kg skater need to exert to melt ice at –10 °C? Is it realistic that the
mechanism for skating is based on pressure?

5. Using Gibbs Helmholtz law calculate (estimate) the freezing point depression and show
that it corresponds to ∆T = 1.86• Osmolality (although Osmolarity works fine for dilute
solutions). Use this to solve for the freezing point depression for 0.154 M NaCl (isotonic
salt solution ~ concentration of physiological solutions). Now obtain the freezing point
depression for 2 M DMSO.

6.    Lever Rule. One result of the HanCRYO2005.pdf paper on the course website is that the
latent heat evolved during phase transition of ice to water is 304 J/g water participating in
the phase change and 233 J/g of eutectic (23.3 % weight salt in solution). Use the lever
rule and existing values in Table 2 to estimate the total latent heat (ice and Eu) for a 15 X
NaCl solution. How would you estimate the latent heat evolution for 2 M DMSO?

7. On the force flux pairing Table given in lecture, what would be the Mechanical term and
accompanying Force and Flux pair?

8. If the Heat of formation of NaCl is -98.2 kcal/mole (exothermic) please estimate the heat
of mixing 0.9 g NaCl into 999.1 g water (this would be to create 0.9% solid fraction in
physiological saline). What does this imply in terms of separation of water entirely from
water during freezing? How much energy would that take?

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