Final answer:
Design a baby warmer that keeps temperatures within a specific range, limits time spent outside of that range, and is cost-effective. Calculate charge and electron flow using relevant formulas, then optimize materials and energy sources to meet designated criteria.
Step-by-step explanation:
The goal is to design a baby warmer that maintains a baby's average temperature in the range of 36.9–37.1°C, spends ≤65 minutes outside the healthy range, and costs ≤$75. To solve for the charge moved by the battery in a bottle warmer, use the formula Q = It, where I is current and t is time. To find the number of electrons flowing per second, use the formula I = nq/t, with n as the number of electrons, q as the charge of an electron (1.6 x 10-19 C), and t as time in seconds.
To calculate the total energy, sum the heat needed to raise the temperature of each material (glass, baby formula, aluminum) using the formula Q = mcΔT, where m is mass, c is specific heat, and ΔT is the change in temperature. Specific heat values are 0.84 J/g°C for glass, 4.18 J/g°C for water (and baby formula), and 0.897 J/g°C for aluminum. By knowing the total energy requirement and the time to heat, design the baby warmer with a cost-effective power source that can supply the necessary current within the target time frame while ensuring safety and efficiency.