Athlete Climbs w/ 4 Potato Chips - Amount Heated 44

[soulja101]

Homework Statement

A)If an athlete (whose mass is 60.0kg) has an energy conversion effiency of 24% and she has an average power of 325W when climbing stairs how high would she be able to climb with the energy consumed from eating 4 potatop chips(28g of chips has 610 kJ of energy and 28g of chips is approximately 15 chips.
B)If the bag of chips in the above questions had been burned and used to heat water from 13degrees celcius to 20 degress celcius, then how much water was being heated(assuming 100%energy conversion)

Homework Equations

Eout/Ein*100%

The Attempt at a Solution

m=60.0kg
Efficiecny=24%
P=325 W

 

[Nate810]

A)Ein= 610 kJ= 6.1*10^6 JEout= Ein*efficiencyEout=6.1*10^6 J *0.24 Eout=1.45*10^6 J Energy consumed from 4 potato chips= 1.45*10^6 JPower=E/tt=E/Pt=1.45*10^6 J /325 Wt=4476.9 secB)Heat energy transferred=mass*Cp*deltaTMass of water=28gCp=4.186J/g*KdeltaT= 20-13=7KHeat energy transferred=28g*4.186J/g*K*7KHeat energy transferred=1130.5 J

 

[m2003]

m(chips)=28g
E(chips)=610 kJ
N(chips)=15

A) To calculate the amount of energy consumed by the athlete from eating 4 potato chips, we can multiply the energy content of one chip (610 kJ/15 chips) by the number of chips consumed (4 chips). This gives us a total energy intake of 162.67 kJ.

Next, we can use the equation Eout/Ein*100% to calculate the height the athlete would be able to climb using this energy. We know that the energy conversion efficiency is 24%, so we can set up the equation as follows:

162.67 kJ/ Ein * 100% = 24%

Solving for Ein, we get Ein = 676.96 kJ.

Now, we can use the formula for potential energy (PE=mgh) to calculate the height (h) the athlete would be able to climb. We know the mass of the athlete (m=60.0kg) and the acceleration due to gravity (g=9.8 m/s^2). Plugging in these values, we get:

PE = 676.96 kJ = mgh

h = 676.96 kJ / (60.0kg * 9.8 m/s^2)

h = 1.16 meters

Therefore, the athlete would be able to climb approximately 1.16 meters using the energy from eating 4 potato chips.

B) To calculate the amount of water being heated, we can use the formula for specific heat (Q=mcΔT), where Q is the heat energy, m is the mass of the water, c is the specific heat capacity of water (4.186 J/g°C), and ΔT is the change in temperature (20°C - 13°C = 7°C).

We know that the energy content of the chips is 610 kJ, and since we are assuming 100% energy conversion, this is the amount of energy being released. Therefore:

610 kJ = mcΔT

m = 610 kJ / (4.186 J/g°C * 7°C)

m = 20.55 g

Therefore, the bag of chips would be able to heat approximately 20.55 grams of water from 13°C to 20°C.