Why Does Evaporation Cool Water?

[Timiop2008]

A puddle of water is on the ground on a sunny day. The energy to break hydrogen bonds between water molecules is 3.4x10^-20J. To evaporate from the surface of the puddle each molecule must break two of these hydrogen bonds.

a) Calculate the difference in internal energy between a water molecule in the liquid and vapour state at the same temperature

b) Calculate the fraction of water molecules with sufficient energy to evaporate a 300K

c) Suggest why the puddles temperature falls during rapid evaporation

d) Suggest another application of cooling by evaporation

The next parts involve the unusually large heat capacity of water

e) the temperature is the same outside and inside a swimming pool on a warm day. You jump in and are surprised to suddenly feel cold even though the temperature still reads the same inside and outside the pool. Explain Why?

f) State and explain two environmental consequences of waters high specific heat capacity

I have absolutely no idea how to go about this question. Any help would be greatly appreciated.

 

[jbsteele]

a) The difference in internal energy between a water molecule in the liquid and vapour state at the same temperature is 6.8x10-20J (3.4x10-20J x 2). b) The fraction of water molecules with sufficient energy to evaporate at 300K can be calculated using the equation: Fraction = e^(-(6.8x10-20J)/(1.38x10-23J/K x 300K)) = 0.0014.c) The puddle's temperature falls during rapid evaporation because the latent heat of vaporization of water is released as the molecules evaporate, cooling the remaining liquid. d) Another application of cooling by evaporation is sweat. Humans use sweat to cool their bodies down by releasing heat through evaporation. e) You feel cold when you jump into the pool because when the body is submerged in water, heat is lost from the body to the water due to the water's high specific heat capacity. This causes the body to cool down even though the temperature inside and outside the pool is the same. f) Two environmental consequences of water's high specific heat capacity are its ability to absorb large amounts of heat without a significant increase in temperature and its ability to moderate temperatures in its surrounding environment. This helps to regulate weather patterns and oceanic cycles.

 

[kerimek]

a) To calculate the difference in internal energy between a water molecule in the liquid and vapor state, we need to use the formula: ΔU = 3/2nRT, where n is the number of moles of water molecules, R is the gas constant (8.314 J/mol⋅K), and T is the temperature in Kelvin (K). Since we are dealing with one water molecule, n = 1. We also know that the energy required to break two hydrogen bonds is 3.4x10^-20J. So, the change in internal energy can be calculated as: ΔU = (3/2)(1)(8.314)(300) - (3.4x10^-20)(2) = 8.2x10^-20 J. This is the difference in internal energy between a water molecule in the liquid and vapor state at the same temperature.

b) To calculate the fraction of water molecules with sufficient energy to evaporate at 300K, we need to use the Boltzmann distribution law: f = e^(-E/kT), where f is the fraction of molecules, E is the energy required for evaporation (3.4x10^-20 J), k is the Boltzmann constant (1.38x10^-23 J/K), and T is the temperature in Kelvin (300K). Therefore, the fraction of water molecules with sufficient energy to evaporate is: f = e^(-3.4x10^-20 / (1.38x10^-23)(300)) = 0.9999999999999999 or approximately 1.

c) The puddle's temperature falls during rapid evaporation because the molecules with the highest energy (and therefore the highest temperature) are the ones most likely to evaporate. As these molecules leave the liquid, the average energy (and therefore the temperature) of the remaining molecules decreases, resulting in a decrease in temperature.

d) Another application of cooling by evaporation is in air conditioning systems. Water is evaporated from a wet surface, such as a cooling coil, to cool the surrounding air. This cooled air is then circulated into a room, providing a cooling effect.

e) The reason for feeling cold when jumping into a swimming pool is due to the high specific heat capacity of water. Water has a higher specific heat capacity than air, meaning it takes more energy to raise the temperature of water compared to air. So