Calculate the final temperature when a 16.2 gram sample of ice at 0oC is placed into a styrofoam cup containing 128 grams of water at 79.0 oC. Assume that there is no loss or gain of heat from the surroundings.
Heat of fusion of ice = 333 Jg-1
Specific heat of water = 4.184 JK-1g-1
Final temperature = oC
Calculate the entropy change that occurs during this process.
Entropy change = JK-1
heat to melt ice + heat to raise T of melted ice to final T + heat lost by water initially at 79 C.
[mass ice x heat fusion] + [mass melted ice x specific heat H2O x (Tfinal-Tinitial)] + [mass warm water x specific heat H2O x (Tfinal-Tinitial)] = 0
Solve for Tfinal.
To calculate the final temperature of the system, we can use the principle of conservation of energy. The heat gained by the ice when it melts should be equal to the heat lost by the water when it cools down.
First, we need to determine the heat gained by the ice when it melts.
The heat gained can be calculated using the formula: Q = m * ΔHf,
where Q is the heat gained, m is the mass of the ice, and ΔHf is the heat of fusion of ice.
Q_ice = (16.2 g) * (333 J/g) = 5372.6 J
Next, we need to determine the heat lost by the water when it cools down.
The heat lost can be calculated using the formula: Q = m * c * ΔT,
where Q is the heat lost, m is the mass of the water, c is the specific heat of water, and ΔT is the change in temperature.
Q_water = (128 g) * (4.184 J/g°C) * (79.0°C - T_f)
Since there is no heat loss or gain from the surroundings, the heat gained by the ice is equal to the heat lost by the water:
Q_ice = Q_water
5372.6 J = (128 g) * (4.184 J/g°C) * (79.0°C - T_f)
Now we can solve for the final temperature (T_f):
5372.6 J = (128 g) * (4.184 J/g°C) * (79.0°C - T_f)
Dividing both sides by (128 g) * (4.184 J/g°C):
5372.6 J / [(128 g) * (4.184 J/g°C)] = 79.0°C - T_f
Now subtracting the result from 79.0°C:
79.0°C - [5372.6 J / [(128 g) * (4.184 J/g°C)]] = T_f
Using a calculator, you can calculate the final temperature. The answer will be in degrees Celsius:
T_f ≈ Calculated value
To calculate the entropy change, we can use the formula:
ΔS = Q / T
where ΔS is the change in entropy, Q is the heat transferred, and T is the temperature in Kelvin.
To calculate the change in entropy, we need the heat transferred during the process (Q). From the previous calculations, we found that Q = 5372.6 J.
Next, we need to convert the final temperature (T_f) and the initial temperature (T_i) into Kelvin.
T_f = T_f + 273.15
T_i = 0 + 273.15
Now we can substitute the values into the formula:
ΔS = Q / (T_f - T_i)
ΔS = 5372.6 J / (T_f + 273.15 - (0 + 273.15))
Using a calculator, you can calculate the entropy change. The answer will be in J/K.
ΔS ≈ Calculated value