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.
To answer both questions, we need to calculate the conversion factors for energy from calories to joules and the amount of energy required to melt ice or vaporize water.
1) Conversion from kilocalories to joules:
1 kilocalorie (kcal) = 4186 joules (J)
To calculate the joules of energy expended during the long walk:
430 kilocalories * 4186 J/kcal = 1,799,480 J
Next, we need to determine the amount of energy required to melt ice:
To convert 0 degrees Celsius ice to water, the ice needs to absorb heat energy to reach its melting point. The specific heat capacity of ice is 2.09 J/g°C, and the latent heat of fusion of water is 334 J/g.
The formula to calculate the energy required is:
Energy = mass * specific heat capacity * ΔT + mass * latent heat of fusion
Since we want to find the mass of ice, mass, in this case, will be the unknown:
Mass * 2.09 J/g°C * (0°C - (-273.15°C)) + Mass * 334 J/g = 1,799,480 J
Simplifying the equation:
Mass * 2.09 * 273.15 + Mass * 334 = 1,799,480
Solving for Mass:
Mass ≈ 2,138 grams or 2.138 kilograms
Since the stomach can hold 1 liter, and 1 liter of water is equal to 1000 grams, the answer is:
2.138 kilograms / 1000 grams ≈ 2.14 liters
Therefore, you would need to consume approximately 2.14 liters of ice water at 0 degrees Celsius to use up the 430 kilocalories of metabolic energy.
2) To calculate the mass of perspiration required to get rid of 240 calories, we first convert calories to joules:
240 calories * 4186 J/calorie = 1,003,440 J
Next, we need to determine the energy required to convert water to vapor:
The latent heat of vaporization of water is given as 2.42 * 10^6 J/kg.
To calculate the mass of perspiration:
Mass * 2.42 * 10^6 J/kg = 1,003,440 J
Solving for Mass:
Mass ≈ 0.414 kilograms or 414 grams
Therefore, one would need to lose approximately 414 grams of perspiration to get rid of the energy from consuming the container of strawberry yogurt.