An ice chest at a beach party contains 12 cans of soda at 4.56 °C. Each can of soda has a mass of 0.35 kg and a specific heat capacity of 3800 J/(kg C°). Someone adds a 6.54-kg watermelon at 28.5 °C to the chest. The specific heat capacity of watermelon is nearly the same as that of water. Ignore the specific heat capacity of the chest and determine the final temperature T of the soda and watermelon in degrees Celsius.
To find the final temperature, we need to use the principle of energy conservation. The energy gained by the soda and watermelon will be equal to the energy lost by the soda. Let's break down the steps to calculate the final temperature:
Step 1: Calculate the initial energy of the soda and watermelon.
- The specific heat capacity (c) of the soda is 3800 J/(kg C°).
- The mass (m) of each soda can is 0.35 kg.
- The initial temperature (T1) of the soda is 4.56 °C.
- The initial energy (E1) of the soda is calculated as: E1 = m * c * T1.
- The specific heat capacity of watermelon is nearly the same as water which is 4186 J/(kg C°).
- The mass of the watermelon is 6.54 kg.
- The initial temperature of the watermelon is 28.5 °C.
- The initial energy (E1) of the watermelon is calculated as: E1 = m * c * T1.
Step 2: Calculate the final energy of the soda and watermelon.
- Let the final temperature of the mixture be T (in °C).
- The mass of the soda-watermelon mixture after combining is 12 * 0.35 kg + 6.54 kg.
- The final energy (E2) of the mixture is calculated as: E2 = (12 * 0.35) * c * T + 6.54 * c * T.
Since energy is conserved, E1 = E2. Setting the equations for the energy of the soda and watermelon mixture equal to each other and solving for T will give us the final temperature (T).
(12 * 0.35) * c * T + 6.54 * c * T = 12 * 0.35 * c * 4.56 + 6.54 * c * 28.5.
Now we can solve this equation to find the final temperature (T) of the soda and watermelon mixture.