Final answer:
To calculate the amount of heat released when 14.6 g of steam at 100 °C hits the skin, condenses, and cools to body temperature of 37 °C, we need to consider the heat absorbed during the phase change and the temperature decrease. The heat released during condensation can be calculated using the heat of vaporization, which is 540 cal/g. The heat released during the temperature decrease can be calculated using the specific heat capacity of water, which is 4.184 J/g °C.
Step-by-step explanation:
To calculate the amount of heat released during the process, we need to consider the heat absorbed during the phase change from steam to liquid water and the heat absorbed during the temperature decrease from 100 °C to 37 °C. First, we need to calculate the heat released during the condensation of steam to liquid water. Given that 540 cal (2260 J) is needed to convert 1 g of water to vapor at 100 °C, we can calculate the heat released during the condensation using the same value. Since the mass of steam is given as 14.6 g, the heat released during condensation is 14.6 g × 2260 J/g = 33,036 J. Next, we need to calculate the heat released during the temperature decrease from 100 °C to 37 °C. The specific heat capacity of water is 4.184 J/g °C. The temperature difference is 100 °C - 37 °C = 63 °C. Using the equation q = m × c × ΔT, where q is the heat, m is the mass, c is the specific heat capacity, and ΔT is the temperature difference, we can calculate the heat released as 14.6 g × 4.184 J/g °C × 63 °C = 3900 J. Finally, we can calculate the total heat released by adding the heat released during condensation and the heat released during the temperature decrease: 33,036 J + 3900 J = 36,936 J. The amount of heat released during this process is 36,936 J.