Question

The label on a soft drink states that 12.0 fl. oz ( 355 g) provides 150. kcal. The drink is cooled to \(10.0^{\circ} \mathrm{C}\) before it is consumed. It then reaches body temperature of \(37.0^{\circ} \mathrm{C}\). Find the net energy content of the drink. (Hint: You can treat the soft drink as being identical to water in terms of heat capacity.)

Short answer

Answer: The net energy content of the soft drink is approximately 595,684.86 Joules.

Step-by-step solution

Convert kcal to Joules

Energy is usually measured in Joules (J). As the initial energy content is given in kilocalories (kcal), we need to convert it to Joules. We know that 1 kcal = 4184 J, so: 150 kcal × (4184 J / 1 kcal) = 627600 J

Calculate the change in temperature

We will need to find the change in temperature, and we can do this by subtracting the initial temperature from the final temperature: ΔT = T_final - T_initial = 37.0°C - 10.0°C = 27.0°C

Calculate heat gained by the drink

With the change in temperature and given mass, we can now find the energy needed to raise the temperature of the drink, using the heat gained formula: Q = mcΔT Where: Q = heat gained (or lost) in Joules (J) m = mass of the drink (water) in grams (g) c = specific heat capacity of the drink (water) in J/g°C (c of water = 4.18 J/g°C) ΔT = change in temperature in °C So, we can plug in the values: Q = (355 g) × (4.18 J/g°C) × (27.0°C) = 31915.14 J

Calculate the net energy content

Now, we can find the net energy content by subtracting the energy gained by the drink (Q) from the initial energy content: Net energy content = Initial energy content - Heat gained Net energy content = 627600 J - 31915.14 J = 595684.86 J So, the net energy content of the drink is approximately 595,684.86 Joules.