During a strenous workout, an athlete generates 1890.0 kj of heat energy. What mass of water would have to evaporate from the athlete's skin to dissipate this much heat?
To calculate the mass of water that would need to evaporate from the athlete's skin to dissipate 1890.0 kJ of heat energy, we can use the formula:
Q = m × L
where:
Q is the heat energy in joules
m is the mass of water in kilograms
L is the latent heat of vaporization for water, which is approximately 2260 kJ/kg
First, let's convert 1890.0 kJ to joules:
Q = 1890.0 kJ × 1000 J/kJ
Q = 1,890,000 J
Now we can rearrange the formula to solve for m:
m = Q / L
m = 1,890,000 J / 2260 kJ/kg
m ≈ 836.28 kg
Therefore, approximately 836.28 kilograms of water would need to evaporate from the athlete's skin to dissipate 1890.0 kJ of heat energy.
To calculate the mass of water that would have to evaporate to dissipate the given amount of heat energy, we need to use the heat of vaporization of water.
The heat of vaporization of water is the amount of heat energy required to convert a given quantity of water from liquid to vapor at a constant temperature and pressure. It is typically given as 40.7 kJ/mol.
To find the mass of water that needs to evaporate, we can use the equation:
q = m × H
where:
- q is the heat energy in joules (given as 1890.0 kJ, which is equivalent to 1890.0 × 10^3 J),
- m is the mass of water in grams,
- H is the heat of vaporization of water in joules per gram (given as 40.7 kJ/mol, which is equivalent to 40.7 × 10^3 J/mol).
First, let's convert the molar heat of vaporization to joules per gram:
- Using the molar mass of water (18 g/mol), we can divide the molar heat of vaporization by the molar mass:
H = 40.7 × 10^3 J/mol / 18 g/mol ≈ 2261.1 J/g
Now, we can rearrange the equation to solve for the mass of water (m):
m = q / H
Substituting the given values:
m = (1890.0 × 10^3 J) / 2261.1 J/g ≈ 837 g
Therefore, approximately 837 grams of water would have to evaporate from the athlete's skin to dissipate 1890.0 kJ of heat energy during the strenuous workout.