In a Styrofoam cup calorimeter, what is the final temperature when 100. g of iron

at 100. ° C is added to 100. g of water at 20. ° C?

heat loss Fe + heat gain by H2O = 0

[massFe x specific heat Fe x (Tfinal-Tinitial)] + [mass H2O x specific heat H2O x (Tfinal-Tinitial)] = 0
Solve for Tfinal

To find the final temperature when iron is added to water in a Styrofoam cup calorimeter, you need to use the principle of conservation of energy. The heat gained by the water and Styrofoam cup must be equal to the heat lost by the iron.

First, you need to calculate the heat gained by the water. To do this, you can use the formula:

Q = mcΔT

Where:
Q is the heat gained or lost (in joules)
m is the mass of the substance (in grams)
c is the specific heat capacity of the substance (water has a specific heat capacity of 4.18 J/g°C)
ΔT is the change in temperature (final temperature - initial temperature)

For the water:
Qwater = mwater * cwater * ΔTwater

substituting the values:
mwater = 100 g
cwater = 4.18 J/g°C
ΔTwater = final temperature - initial temperature = final temperature - 20°C

Next, you need to calculate the heat lost by the iron. Since the specific heat capacity of iron varies with temperature, you need to use a different formula:

Q = mcΔT

Where:
Q is the heat gained or lost (in joules)
m is the mass of the substance (in grams)
c is the specific heat capacity of the substance at a given temperature
ΔT is the change in temperature (final temperature - initial temperature)

For the iron:
Qiron = miron * ciron * ΔTiron

Substituting the values:
miron = 100 g
ciron = 0.45 J/g°C (specific heat capacity of iron at 100°C)
ΔTiron = final temperature - initial temperature = final temperature - 100°C

Now, according to the principle of conservation of energy, the heat lost by the iron is equal to the heat gained by the water:

Qwater = -Qiron

mwater * cwater * ΔTwater = -miron * ciron * ΔTiron

Solving for the final temperature:
final temperature = (mwater * cwater * ΔTwater) / (miron * ciron) + initial temperature

Plugging in the given values:
final temperature = (100 g * 4.18 J/g°C * (final temperature - 20°C)) / (100 g * 0.45 J/g°C) + 100°C

Simplifying the equation, you can solve for the final temperature. However, please note that the algebraic manipulation gets quite complicated, and it is best to use a numerical method or a scientific calculator to find the final temperature.