42-101
Intro to BME (Przybycien)
Spring
2005
PROBLEM
SET No. 6
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Posted: |
2/24/05 |
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Due: |
3/18/05 in class |
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Org Task |
Interim Team Evaluation in class
on Wed, 3/2/05 |
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1. |
Energy Balances. A yeast growing aerobically on glucose exhibits the growth stoichiometry below: C6H12O6 + 3O2 + 0.48NH3 ® 0.48C6H10NO3 + 4.32H2O + 3.12CO2 Note that stoichiometric equations for cell growth represent cells in terms of dry cell mass. A yield coefficient, YD, can be written for the heat released by growing cells just as they can be written to track the relationships between nutrients consumed and products released. For cells growing on glucose, YD is roughly 0.42 g dry cells/kcal heat released. A 15 L (liquid volume) batch fermentation is run with the yeast described
above. The fermentation is started
with 26.0±0.2
grams glucose (avg
±
std dev) and 0.25±0.03 grams of wet
cell mass. If the fermenter
loses half of the heat generated by the growing yeast to the surroundings,
what would the change in the temperature, in degrees celsius,
of the liquid in the fermenter be from the start to
the finish of the fermentation? Report
result as the average ± one standard deviation. You may assume that the fermentation broth
has the physical and thermal properties of water for the purposes of this
problem and that the fermentation starts at a broth temperature of 25°C. |
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2. |
Energy Balances. MMD text
chapter 4, problem 4. |
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3. |
Bioenergetics. An negatively charged nutrient (equivalent charge of one electron) is actively transported from the outside to the inside of a cell membrane; i.e. a cell captures energy from the hydrolysis of ATP in order to bring a molecule from the outside of the cell, where it is present at a low concentration, to the inside of the cell, where it is present at higher concentration. If the molecular species to be transported is present at a concentration of 34.5 nM on the outside of the cell, the potential on the outside of the cell is +75 mV, the potential on the inside of the cell is -35 mV, and the efficiency at which energy from the hydrolysis of ATP is captured for this active transport process is 59%, what is the maximum concentration of the transported species that may be achieved inside the cell? [The gas constant may be taken at 1.987 cal/(mol·K)] |
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4. |
Bioenergetics. A pediatric blood pump (left ventricular assist device or LVAD) is designed to circulate blood at a rate of 3.2L/min. The expected inlet pressure is 7 mmHg and the expected outlet pressure is 82 mmHg. The inlet vessel diameter is 6.0 mm; the outlet vessel diameter is 4.5 mm. a. What would be the linear velocities, in cm/s, of the blood flow on the inlet and outlet sides of the pump? b. What would be the power output, in c. If the pump is driven with a small DC motor that is 38% efficient, how many current capacity in milliamp*hours (mA·h) must a 6 V battery have to operate the pump continuously for 5 days without recharging? d. Suppose 6 V batteries with the current capacity calculated above
in part c were available and that the manufacturer indicated that of their
production run of the battery, the standard deviation in the actual capacity
was found to be 0.7% of the total capacity.
Calculate the minimum time, in hours, that the pediatric LVAD should
be operated between battery changes at the 99.9999% confidence level (i.e.
one chance in a million that the battery would run out before a change). |
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5. |
Binding. MMD text chapter 5,
problem 1. |
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6. |
Binding. MMD text chapter 5,
problem 2. |
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Updated on 2/24/05 by TMP