suppose 2 45g if ice cubes are added in a glass containing 500cm^3 of cola at 20°C. When the thermal equibruim is reached all the ice will.have melted and the temperature of the mixture will be somewhere between 20°C and 0 °C . Calculate the final temperatureof the mixture
(2.45 g ice x heat fusion ice) + [(2.45 g H2O x specific heat H2O x (Tfinal-Tinitial)] + ([(500 g cola x specific heat cola x (Tfinal-Tinitial)] = 0
Substitute and solve for Tfinal
Post your work if you get stuck.
To calculate the final temperature of the mixture, we can use the principles of heat transfer and the concept of specific heat capacity.
First, let's calculate the heat absorbed or released by the cola and the ice during the process.
1. Heat absorbed by the cola (Q₁):
The formula to calculate heat is Q = mcΔT, where Q is the heat, m is the mass, c is the specific heat capacity, and ΔT is the change in temperature.
Given:
- Mass of cola: 500 cm³ (which is equal to 500 g, as 1 cm³ of cola has a density equal to 1 g/cm³)
- Initial temperature of cola: 20°C
- Specific heat capacity of cola: let's assume it to be 4.18 J/g°C (which is approximately the specific heat capacity of water)
Calculating Q₁:
Q₁ = mcΔT
Q₁ = 500 g * 4.18 J/g°C * (final temperature - 20°C)
2. Heat released by the ice (Q₂):
The heat released by the ice while melting is calculated using the formula Q = mL, where Q is the heat, m is the mass, and L is the heat of fusion.
Given:
- Mass of ice cubes: 2 * 45 g = 90 g
- Heat of fusion for ice (L): 334 J/g
Calculating Q₂:
Q₂ = mL
Q₂ = 90 g * 334 J/g
Since the system is thermally isolated, the heat absorbed by the cola (Q₁) should be equal to the heat released by the ice (Q₂).
Q₁ = Q₂
500 g * 4.18 J/g°C * (final temperature - 20°C) = 90 g * 334 J/g
Now, we can solve this equation to find the final temperature (T₂) of the mixture.
500 * 4.18 * (final temperature - 20) = 90 * 334
Simplifying the equation further:
2090 * (final temperature - 20) = 30060
final temperature - 20 = 30060 / 2090
final temperature - 20 ≈ 14.40°C
Adding 20 to both sides:
final temperature ≈ 14.40°C + 20°C
final temperature ≈ 34.40°C
Therefore, the final temperature of the mixture will be approximately 34.40°C.