The label on a soft drink states that 11 fl. oz (325 g) provides 285 kcal. The drink is cooled to 12.0°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.)
I'm not sure how 285 kcal works into solving this, or how to get started. Thank you for any help!
The 285 kcal represents chemical energy released when the contents are consumed. There is an additional transfer of energy to the drink from the body as the soft drink warms up to body temperature:
(1.00 cal/g*C)*25 C*325 g = 8.13 kcal
The net energy content of the cold drink is 285 - 8 = 278 kcal
thank you for your help!
To find the net energy content of the drink, we need to consider the changes in temperature it undergoes. Here's how you can approach this problem:
Step 1: Calculate the heat gained by the drink to reach body temperature.
- The specific heat capacity of water is approximately 4.18 J/g°C.
- The mass of the drink is given as 325 g.
- The initial temperature of the drink is 12.0°C.
- The final temperature of the drink when it reaches body temperature is 37°C.
The formula for calculating heat is: Q = mcΔT, where Q is the heat gained, m is the mass, c is the specific heat capacity, and ΔT is the change in temperature.
Using this formula, you can calculate the heat gained by the drink to reach body temperature:
Q1 = mcΔT1
Q1 = (325 g)(4.18 J/g°C)(37°C - 12.0°C)
Step 2: Convert the heat gained to kilocalories (kcal).
- 1 kcal = 4184 J
To convert the heat gained to kcal, divide the result from step 1 by 4184:
Q1 (in kcal) = Q1 (in J) / 4184
Step 3: Subtract the energy content stated on the label from the calculated heat to find the net energy content of the drink.
- The energy content stated on the label is given as 285 kcal.
Net energy content = Q1 (in kcal) - 285 kcal
Solving these steps will give you the net energy content of the drink.