Under normal conditions the human heart converts about 13.0 J of chemical energy
body. (a) Determine the number of Calories required to power the heart for one day,
per second into 1.30 W of mechanical power as it pumps blood throughout the
given that 1 Calorie equals 4 184 J. (b) Metabolizing 1.00 kg of fat can release
about 9.00 x 103 Calories of energy. What mass of metabolized fat would power
the heart for one day?
3g
(a) Well, let's get our heart pumping! To determine the number of Calories required to power the heart for one day, we need to multiply the power per second by the number of seconds in a day. So, 1.30 W multiplied by 24 hours (that's 24 hours x 60 minutes x 60 seconds) will give us the energy needed per day in joules. But since we're dealing with Calories, we need to divide that value by 4184 J/Cal. Math time!
1.30 W * 24 hours * 60 minutes * 60 seconds / 4184 J/Cal = a number of Calories that's as hard to calculate as solving a Rubik's Cube while blindfolded. So here's the solution: approximately 111.65 Calories per day to keep that heart pumping like a champ!
(b) Alright, let's break out the fat reserves to power that heart. If 1.00 kg of fat can release about 9.00 x 103 Calories of energy, then we can use the energy requirement from part (a) to figure out the mass of metabolized fat needed.
Mass of fat = Energy requirement / Energy released per kg of fat
Mass of fat = 111.65 Calories / (9.00 x 103 Calories/kg)
Dividing those numbers should give you the mass of fat needed to power the heart for one day. It's like feeding the heart's fuel tank!
To determine the number of Calories required to power the heart for one day, we need to calculate the total energy used by the heart per day and then convert it to Calories.
(a) First, let's find the total energy used by the heart per day. We are given that the heart converts 13.0 J of chemical energy per second into 1.30 W of mechanical power. This means every second, the heart converts 13.0 J of chemical energy into mechanical work.
To calculate the energy used per day, we need to multiply the energy used per second by the number of seconds in a day. There are 24 hours in a day, 60 minutes in an hour, and 60 seconds in a minute, so:
Energy used per day = (Energy used per second) x (seconds in a day)
= 13.0 J/s * 24 * 60 * 60 s/day
Now, we can convert this energy from joules to Calories. We know that 1 Calorie is equal to 4,184 J:
Energy used per day (in Calories) = (Energy used per day) / (1 Calorie/4184 J)
(b) To find the mass of metabolized fat that would power the heart for one day, we need to know how many Calories are released by metabolizing 1.00 kg of fat. We are given that metabolizing 1.00 kg of fat releases about 9.00 x 10^3 Calories of energy.
To calculate the mass of metabolized fat that would power the heart for one day, we need to divide the energy required per day (in Calories) by the energy released per kg of fat (in Calories/kg):
Mass of metabolized fat = (Energy used per day in Calories) / (Energy released per kg of fat in Calories/kg)
Now, we can substitute the values we calculated in part (a) and the information given in part (b) to find the answer.