Determine the final temp when 45.8g of aluminum at -5.2C is added to a mixture of 45.0g of ice at 0C and 2000g of water at 95C?

[45.8 g Al x specific heat Al x (Tf -Ti)]+ [45 g ice x heat fusion ice]+[45 g H2O from melted ice x specific heat water x (Tf - Ti)] + [2000 g H2O x specific heat water x (Tf-Ti)] = 0

Tf = final T; Ti = initial T. Solve for Tf. Post your work if you get stuck.

I know the specific heat for water is 4.184 and Al is 0.900. I don't know ice - our professor never went over that. Is it the same as water, or different?

No it isn't; however, you don't need the specific heat of ice since the temperature of the ice is listed as zero C. What you need is the heat of fusion (to melt the ice) and that is 334 J/g.

che che che chiia

To determine the final temperature when substances at different temperatures are combined, we can use the principle of conservation of energy, specifically the equation:

heat gained by substance A = heat lost by substance B

In this case, substance A is the aluminum and substance B is the ice and water mixture. We will calculate the heat gained by the aluminum and the heat lost by the ice and water mixture, and then equate them to find the final temperature.

First, let's calculate the heat gained by the aluminum.

Q_aluminum = mass_aluminum * specific heat capacity_aluminum * (final temperature - initial temperature)

The specific heat capacity of aluminum is 0.897 J/g°C.

Q_aluminum = 45.8g * 0.897 J/g°C * (final temperature - (-5.2°C))
Q_aluminum = 45.8g * 0.897 J/g°C * (final temperature + 5.2°C)

Next, let's calculate the heat lost by the ice and water mixture.

Q_ice = mass_ice * specific heat capacity_ice * (final temperature - initial temperature)
Q_water = mass_water * specific heat capacity_water * (final temperature - initial temperature)

The specific heat capacity of ice is 2.09 J/g°C, and the specific heat capacity of water is 4.18 J/g°C.

Q_ice = 45.0g * 2.09 J/g°C * (final temperature - 0°C)
Q_water = 2000g * 4.18 J/g°C * (final temperature - 95°C)

Since the ice will initially melt before reaching the final temperature, we also need to account for the heat required to melt the ice. The heat of fusion for ice is 334 J/g.

Q_ice_fusion = mass_ice * heat of fusion
Q_ice_fusion = 45.0g * 334 J/g

Now, let's equate the heat gained by the aluminum to the heat lost by the ice and water mixture.

Q_aluminum = Q_ice + Q_water + Q_ice_fusion

Substitute the previously calculated expressions:

45.8g * 0.897 J/g°C * (final temperature + 5.2°C) = 45.0g * 2.09 J/g°C * (final temperature - 0°C) + 2000g * 4.18 J/g°C * (final temperature - 95°C) + 45.0g * 334 J/g

Simplify and solve the equation to find the value of the final temperature.