Substances with a high heat capacity (such as water) are able to absorb signific

Question

Substances with a high heat capacity (such as water) are able to absorb significant amounts of heat with a minimal change in temperature. When we measure the heat capacity of a substance, we are measuring the amount of heat required to raise the temperature of a defined mass (e.g., 1 gram) of that substance 1 degree C. The heat capacity of freshwater is exactly 1 calorie per gram (cal/g). This nice round number is no coincidence - a calorie is defined as the amount of heat required to raise 1 gram of liquid water 1 degree C. Another property of water is its latent heat of vaporization. Water has a very high latent heat of vaporization of540 calories. This means that in order for 1 gram of water already at a temperature of 100 degree C to actually boil and change to vapor, the water molecules must absorb 540 calories of heat. If the steam then cools and condenses back to liquid, it will release an equivalent amount of heat energy (-540 calories). Due to waters heat capacity, it takes even more heat for water to evaporate at temperatures below the boiling point. At a typical temperature for tropical waters during hurricane season, the latent heat of evaporation is 575 cal/g. Hurricanes are therefore powered by the release of heat as water vapor condenses in the atmosphere (due to the evaporation of warm surface waters). In a single day, a typical hurricane may release 1.80 times 10^18 cal of energy. What volume of water (in m^3) must be evaporated from the ocean's surface in order to provide this energy? Assume an average density of seawater of 1.0278 g/cm^3 and the latent heat of evaporation of 575 cal/g.

Explanation / Answer

1. Amount of heat released by hurricane Q=1.8*10^18cal

Latent heat of evaporation L= 575 cal/g

Mass of water m=??

Since Q=m*L

1.8*10^18cal=m*575 cal/g

3.13*10^-3*10^18=m

m=3.13*10^15g

We know that density=mass/volume

density of sea water=1.0278g/cm3

mass of sea water=3.13*10^15g

Now volume=mass/density

=3.13*10^15g/1.0278g/cm3

=3.045*10^15cm3

=3.045*10^9m3

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