few other questions.
1.) Suppose you expend 430 kilocalories during a long walk, how many liters of ice water at 0 degrees do you need to consume in order to use up the 430 kilocalories of metabolic energy. Stomach can hold 1 liter.
2. A person eats a container of strawberry yogurt. The Nutritional Facts label states that it contains 240 calories (a calorie = 4186 J). What mass of perspiration would one have to lose to get rid of this energy. Latent heat of vaporization of water is 2.42*10^6.
430kcal=Mass*1kilocal/kg*(37-0)
masswater= 430kg/37
assume denstiy water is 1kg/liter
so that is 430/37 liters
2. 240*4186J=2.42E6J/kg*mass water
solve for mass of sweat.
To answer the first question, we need to calculate the amount of ice water at 0 degrees Celsius required to consume 430 kilocalories of metabolic energy.
Step 1: Convert kilocalories to calories
1 kilocalorie = 1000 calories
So, 430 kilocalories = 430,000 calories
Step 2: Convert calories to joules
1 calorie = 4186 J
So, 430,000 calories = 430,000 * 4186 J = 1,799,080,000 J
Step 3: Calculate the heat transfer when consuming ice water
The heat transfer equation is given by Q = m * c * ΔT, where:
Q is the heat transfer (in joules),
m is the mass of the substance (in grams),
c is the specific heat capacity (in J/g·°C),
ΔT is the change in temperature (in °C).
In this case, the change in temperature (ΔT) is from 0°C to body temperature (approximately 37°C).
Step 4: Calculate the mass of ice water
We need to find the mass (m) of ice water. By assuming the specific heat capacity of water (c) is 4.18 J/g·°C.
Q = m * c * ΔT
1,799,080,000 J = m * 4.18 J/g·°C * (37°C - 0°C)
Simplifying the equation:
1,799,080,000 J = m * 4.18 J/g·°C * 37°C
Divide both sides by (4.18 * 37):
m = 1,799,080,000 J / (4.18 J/g·°C * 37°C)
m ≈ 12,485,724 grams ≈ 12,485.724 kg
Since 1 liter of water has a mass of 1000 grams (1 kg), we need approximately 12,485.724 liters of ice water at 0 degrees Celsius to consume 430 kilocalories of metabolic energy during a long walk.
Moving on to the second question, we need to calculate the mass of perspiration required to get rid of 240 calories of energy.
Step 1: Convert calories to joules
1 calorie = 4186 J
So, 240 calories = 240 * 4186 J = 1,004,640 J
Step 2: Calculate the mass of perspiration
The heat transfer equation is Q = m * ΔHv, where:
Q is the heat transfer (in joules),
m is the mass of the substance (in grams),
ΔHv is the enthalpy of vaporization or latent heat of vaporization (in J/g).
In this case, the enthalpy of vaporization (ΔHv) of water is 2.42*10^6 J/g.
Step 3: Calculate the mass of perspiration
Q = m * ΔHv
1,004,640 J = m * 2.42*10^6 J/g
Simplifying the equation:
m = 1,004,640 J / (2.42*10^6 J/g)
m ≈ 0.415 grams
Therefore, one would need to lose approximately 0.415 grams of perspiration to get rid of the energy obtained from eating the container of strawberry yogurt.