A person ate 0.50 pound of cheese (an energy intake of \(4000 \mathrm{~kJ}\) ). Suppose that none of the energy was stored in his body. What mass (in grams) of water would he need to perspire in order to maintain his original temperature? (It takes \(44.0 \mathrm{~kJ}\) to vaporize 1 mole of water.

Understanding the concept of energy intake calculation is crucial in various fields of science, particularly in chemistry and biology. Calories or joules are the units typically used to quantify the energy contained in food. Energy intake refers to the amount of energy that a person consumes through eating and drinking. In our exercise, the person has an energy intake of 4000 kJ from consuming 0.5 pounds of cheese.

To maintain the body's original temperature after this caloric intake, the body would need to dispel excess energy. A common way the body does this is through perspiration, where water is vaporized to remove heat from the body. The associated heat loss must match the energy intake to maintain a stable internal temperature. Therefore, calculating the energy intake allows us to determine the amount of water the body needs to vaporize to balance the energy equation.

This ties in directly with the idea that energy can neither be created nor destroyed; it can only be converted from one form to another, a principle known as the first law of thermodynamics.

When discussing moles of water vaporization, we refer to the amount of water (in moles) that needs to be converted into vapor to achieve a certain energy transfer. The concept of a mole is a fundamental cornerstone in chemistry because it is a unit that allows chemists to connect the number of particles (atoms, molecules, etc.) with mass.

To calculate the moles of water vaporized, we need to understand the concept of latent heat of vaporization, which is the energy required to change a substance from a liquid to a gas state without changing its temperature. Our exercise specifies that it takes 44.0 kJ to vaporize 1 mole of water. By dividing the total energy intake in joules by the energy required to vaporize one mole of water, we arrive at the number of moles that have been vaporized to dissipate the excess energy. This step is pivotal because it quantifies the chemical process of perspiration in terms of moles, thereby linking the physiological action to a measureable chemical quantity.

The molar mass of water is an essential constant in chemistry that denotes the mass of one mole of water molecules. The molar mass is the sum of the atomic masses of all the atoms in a molecule. For water (H₂O), with two hydrogen atoms (each approximately 1 gram per mole) and one oxygen atom (approximately 16 grams per mole), the molar mass comes to about 18 grams per mole.

The importance of understanding the molar mass lies in its ability to convert between moles and grams, which is a common task in chemistry. In the context of our exercise, once we have calculated the moles of water vaporized to balance the energy intake, we use the molar mass of water to convert this number into grams. This gives us a tangible quantity that can be related to the real-world phenomenon of sweating. It also highlights the practical application of theoretical chemical concepts to biological processes and helps students visualize the scale of chemical reactions in everyday life.