The label on a soft drink states that 15 fl. oz (444 g) provides 170 kcal. The drink is cooled to 11.0°C before it is consumed. It then reaches body temperature of 37°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.)
To find the net energy content of the drink, we need to calculate the change in energy or heat gained or lost by the drink as it goes from being cooled to body temperature.
The change in energy can be calculated using the formula:
ΔQ = mcΔT
Where:
ΔQ = change in energy (in joules, J)
m = mass of the drink (in grams, g)
c = specific heat capacity of the drink (in J/g°C)
ΔT = change in temperature (in °C)
First, we need to find the change in temperature (ΔT) of the drink. It goes from 11.0°C (cooled) to 37°C (body temperature), so:
ΔT = 37°C - 11.0°C = 26.0°C
Next, we need to determine the mass of the drink. The label states that 15 fl. oz (fluid ounces) of the drink weighs 444 grams. Since 1 fluid ounce is approximately 29.57 grams, we can calculate the mass of the drink as:
Mass = 15 fl. oz * 29.57 g/fl. oz = 443.55 g ≈ 444 g
Now, we need to assume that the soft drink has the same specific heat capacity as water. The specific heat capacity of water is approximately 4.18 J/g°C.
Using the values we have:
ΔQ = mcΔT
ΔQ = 444 g * 4.18 J/g°C * 26.0°C
ΔQ ≈ 46,776 J (joules)
Finally, we need to convert the energy from joules to kilocalories (kcal). Since 1 kcal is approximately equal to 4.184 kJ, we have:
Net Energy Content = ΔQ / 4.184 kJ/kcal
Net Energy Content ≈ 46,776 J / 4.184 kJ/kcal ≈ 11.19 kcal
Therefore, the net energy content of the drink is approximately 11.19 kcal.