Evaporating sweat cools the body because evaporation is an endothermic process: H2O(l) → H2O(g) ΔH°rxn = +44.01 kJ. Estimate the mass of water that must evaporate from the skin to cool the body by 0.50°C. Assume a body mass of 95 kg and assume that the specific heat capacity of the body is 4.0 J/g°C.

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Calculate the total heat energy (q) required to cool the body by 0.50°C using the formula q = m * c * ΔT, where m is the mass of the body in grams, c is the specific heat capacity, and ΔT is the change in temperature.

Convert the body mass from kilograms to grams by multiplying by 1000, since 1 kg = 1000 g.

Substitute the values into the formula: m = 95000 g (since 95 kg = 95000 g), c = 4.0 J/g°C, and ΔT = 0.50°C.

Calculate the heat energy (q) in joules required to cool the body by 0.50°C.

Use the enthalpy change of the evaporation process (ΔH°rxn = +44.01 kJ/mol) to find the mass of water that must evaporate. Convert q from joules to kilojoules, then divide by ΔH°rxn to find the number of moles of water that need to evaporate. Finally, multiply by the molar mass of water (18.02 g/mol) to find the mass of water in grams.

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Endothermic Process

An endothermic process is a chemical reaction or physical change that absorbs heat from its surroundings. In the context of evaporation, when water transitions from liquid to gas, it requires energy, which is taken from the skin, resulting in a cooling effect. This is quantified by the enthalpy change (ΔH°rxn), which indicates the amount of heat absorbed during the phase change.

Specific Heat Capacity

Specific heat capacity is the amount of heat required to raise the temperature of a unit mass of a substance by one degree Celsius. For the human body, a specific heat capacity of 4.0 J/g°C means that it takes 4.0 joules of energy to increase the temperature of 1 gram of body mass by 1°C. This concept is crucial for calculating how much energy is needed to cool the body by a specific temperature change.

Mass-Energy Relationship

The mass-energy relationship in thermodynamics relates the mass of a substance to the energy required for a phase change or temperature change. In this scenario, the mass of water that must evaporate can be calculated using the formula Q = mcΔT, where Q is the heat absorbed, m is the mass of water, c is the specific heat capacity, and ΔT is the change in temperature. This relationship allows us to estimate the amount of water needed to achieve the desired cooling effect.

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