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Chemistry / Elementary Principles of Chemical Processes 4 / Chapter 7.8 / Problem 7.25

Elementary Principles of Chemical Processes | 4th Edition | ISBN: 9780470616291 | Authors: Richard M. Felder Ronald W. Rousseau, Lisa G. Bullard

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The heart pumps blood at an average rate of 5 L/min. The gauge pressure on the venous

Chapter 7, Problem 7.25

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QUESTION:

The heart pumps blood at an average rate of 5 L/min. The gauge pressure on the venous (intake) side is 0 mm Hg and that on the arterial (discharge) side is 100 mm Hg. Energy is supplied to the heart as heat released by the absorption of oxygen in the cardiac muscles: 5 mL (STP) O2/min is absorbed, and 20.2 J is released per mL of O2 absorbed. Part of this absorbed energy is converted to flow work (the work done to pump blood through the circulatory system), and the balance is lost as heat transferred to the tissues surrounding the heart. (a) Simplify Equation 7.4-12 for this system, assuming (among other things) that there is no change in internal energy from inlet to outlet. (b) What percentage of the heat input to the heart Q_ in is converted to flow work? (The answer may be thought of as the efficiency of the heart as a pump.)

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QUESTION:

The heart pumps blood at an average rate of 5 L/min. The gauge pressure on the venous (intake) side is 0 mm Hg and that on the arterial (discharge) side is 100 mm Hg. Energy is supplied to the heart as heat released by the absorption of oxygen in the cardiac muscles: 5 mL (STP) O2/min is absorbed, and 20.2 J is released per mL of O2 absorbed. Part of this absorbed energy is converted to flow work (the work done to pump blood through the circulatory system), and the balance is lost as heat transferred to the tissues surrounding the heart. (a) Simplify Equation 7.4-12 for this system, assuming (among other things) that there is no change in internal energy from inlet to outlet. (b) What percentage of the heat input to the heart Q_ in is converted to flow work? (The answer may be thought of as the efficiency of the heart as a pump.)

ANSWER:

Step 1 of 3

This problem is an example of part of the metabolic system all our bodies go through. Assume there is only one output and one input stream and the mass flow is constant across the system (there is no blood accumulation in the heart itself), then open system energy balance is

Here

is rate of heat absorbed by the system from surroundings

is shaft work done by the system on the surroundings.

is change in specific internal energy, kinetic energy,

is pressure,

is specific molar volume,

is velocity, and is a change in height.

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