The heat of fusion of water is 80 cal/g. When 25 g of ice at 0ºC is placed in the contents of a 12 oz can of Coke (≈350 g) at 25ºC, what is the final temperature of the beverage?
If 25g of ice were to melt, 80*25 = 2000 calories would be removed from the Coke. To cool 350 g of Coke from 25 C to 0 C would required removing 8750 calories from the Coke. Therefore all of the ice will melt, and then heat up from 0C, while the Coke will be cooled to an intermediate temperature, T. To solve for that temperature, assume that all heat gained by the ice and water as it heats up equals the heat lost by the Coke.
80*25 + 80*1*(T-0) = 350*1*(25 - T)
2000 + 80T = 8750 -350 T
430T = 6750
T = 15.7 C
To find the final temperature of the beverage, we can use the principle of conservation of energy.
Step 1: Calculate the heat gained by the ice:
The heat gained by the ice can be calculated using the formula Q = m * Hf, where Q is the heat gained, m is the mass of the ice, and Hf is the heat of fusion of water.
Q = 25 g * 80 cal/g
Q = 2000 cal
Step 2: Calculate the heat lost by the beverage:
The heat lost by the beverage can be calculated using the formula Q = m * c * ΔT, where Q is the heat lost, m is the mass of the beverage, c is the specific heat capacity of the beverage, and ΔT is the change in temperature.
Q = 350 g * c * (T - 25ºC), where T is the final temperature of the beverage.
Step 3: Set the heat gained by the ice equal to the heat lost by the beverage:
2000 cal = 350 g * c * (T - 25ºC)
Step 4: Solve for the final temperature of the beverage:
Divide both sides of the equation by 350 g * c:
(T - 25ºC) = 2000 cal / (350 g * c)
Assuming the specific heat capacity of the beverage is approximately 1 cal/gºC, we can simplify the equation to:
(T - 25ºC) = 5.71ºC
Solving for T:
T = 25ºC + 5.71ºC
T ≈ 30.71ºC
Therefore, the final temperature of the beverage is approximately 30.71ºC.
To find the final temperature of the beverage, we need to consider the heat gained by the ice and the heat lost by the Coke. We'll assume no heat is transferred to the surrounding environment.
Here's how we can calculate it:
1. Calculate the heat gained by the ice:
- The mass of ice is given as 25 g.
- The heat of fusion of water is given as 80 cal/g.
- So, the heat gained by the ice can be calculated as: mass of ice * heat of fusion of water.
- Heat gained by ice = 25 g * 80 cal/g.
2. Calculate the heat lost by the Coke:
- The mass of the Coke is given as 350 g.
- We assume its specific heat capacity is the same as water, which is 1 cal/g·°C.
- The initial temperature of the Coke is given as 25ºC, and we need to find the final temperature.
- So, the heat lost by the Coke can be calculated as: mass of Coke * specific heat capacity of water * (final temperature - initial temperature).
- Heat lost by Coke = 350 g * 1 cal/g·°C * (final temperature - 25ºC).
3. Equate the heat gained by the ice to the heat lost by the Coke and solve for the final temperature:
- Heat gained by ice = Heat lost by Coke.
- 25 g * 80 cal/g = 350 g * 1 cal/g·°C * (final temperature - 25ºC).
- Simplify and solve for the final temperature.
After performing the calculations, the final temperature of the beverage can be determined.