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3. Assuming that there are 5 x 1013 cells in the human body and that ATP is turning over at a rate of 10⁹ ATP per minute in each cell, how many watts is the human body consuming (a watt is a joule per second, and there are 4.18 joules/calorie). Assume that hydrolysis of ATP yields 10 kcal/mol.

3. Assuming that there are 5 x 1013 cells in the human body and that ATP is turning over at a rate of 10⁹ ATP per minute in each cell, how many watts is the human body consuming (a watt is a joule per second, and there are 4.18 joules/calorie). Assume that hydrolysis of ATP yields 10 kcal/mol.

Biochemistry
Biochemistry
9th Edition
ISBN:9781319114671
Author:Lubert Stryer, Jeremy M. Berg, John L. Tymoczko, Gregory J. Gatto Jr.
Publisher:Lubert Stryer, Jeremy M. Berg, John L. Tymoczko, Gregory J. Gatto Jr.
Chapter1: Biochemistry: An Evolving Science
Section: Chapter Questions
Problem 1P
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**Problem 3: Energy Consumption by the Human Body** Assuming that there are \(5 \times 10^{13}\) cells in the human body and that ATP is turning over at a rate of \(10^9\) ATP per minute in each cell, how many watts is the human body consuming? (Note: A watt is a joule per second, and there are 4.18 joules per calorie). Assume that hydrolysis of ATP yields 10 kcal/mol. **Solution Explanation** To calculate the power consumption in watts, follow these steps: 1. **Total ATP Molecules Turned Over Per Minute:** - Total cells in the human body: \(5 \times 10^{13}\) - ATP turnover rate per cell per minute: \(10^9\) - Total ATP turnover per minute for the entire body = \(5 \times 10^{13} \times 10^9\) 2. **Energy Yield from ATP Hydrolysis:** - 1 mol of ATP yields 10 kcal. - Convert kcal to calories: \(10 \text{ kcal} = 10,000 \text{ cal}\). 3. **Energy in Joules:** - Convert calories to joules using \(1 \text{ cal} = 4.18 \text{ joules}\). - Therefore, \(10,000 \text{ cal} \times 4.18 \text{ joules/cal} = 41,800 \text{ joules/mol}\). 4. **Moles of ATP per Minute:** - Avogadro's number: \(6.022 \times 10^{23}\) molecules/mol. - Moles of ATP hydrolyzed per minute = \(\frac{Total \, ATP}{6.022 \times 10^{23}}\). 5. **Energy per Minute in Joules:** - Calculate total energy consumed per minute in joules using the energy per mole (41,800 joules/mol). 6. **Convert to Power (Watts):** - Since power is energy per second, divide the total joules per minute by 60 to convert to joules per second (watts). This detailed explanation helps in understanding how energy consumption is calculated in the human body based on ATP turnover rates.
Transcribed Image Text:**Problem 3: Energy Consumption by the Human Body** Assuming that there are \(5 \times 10^{13}\) cells in the human body and that ATP is turning over at a rate of \(10^9\) ATP per minute in each cell, how many watts is the human body consuming? (Note: A watt is a joule per second, and there are 4.18 joules per calorie). Assume that hydrolysis of ATP yields 10 kcal/mol. **Solution Explanation** To calculate the power consumption in watts, follow these steps: 1. **Total ATP Molecules Turned Over Per Minute:** - Total cells in the human body: \(5 \times 10^{13}\) - ATP turnover rate per cell per minute: \(10^9\) - Total ATP turnover per minute for the entire body = \(5 \times 10^{13} \times 10^9\) 2. **Energy Yield from ATP Hydrolysis:** - 1 mol of ATP yields 10 kcal. - Convert kcal to calories: \(10 \text{ kcal} = 10,000 \text{ cal}\). 3. **Energy in Joules:** - Convert calories to joules using \(1 \text{ cal} = 4.18 \text{ joules}\). - Therefore, \(10,000 \text{ cal} \times 4.18 \text{ joules/cal} = 41,800 \text{ joules/mol}\). 4. **Moles of ATP per Minute:** - Avogadro's number: \(6.022 \times 10^{23}\) molecules/mol. - Moles of ATP hydrolyzed per minute = \(\frac{Total \, ATP}{6.022 \times 10^{23}}\). 5. **Energy per Minute in Joules:** - Calculate total energy consumed per minute in joules using the energy per mole (41,800 joules/mol). 6. **Convert to Power (Watts):** - Since power is energy per second, divide the total joules per minute by 60 to convert to joules per second (watts). This detailed explanation helps in understanding how energy consumption is calculated in the human body based on ATP turnover rates.
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