A student heats 64.05 grams of nickel to 97.80 °C and then drops it into a cup containing 81.11 grams of water at 21.79 °C. She measures the final temperature to be 27.84 °C.
The heat capacity of the calorimeter (sometimes referred to as the calorimeter constant) was determined in a separate experiment to be 1.50 J/°C.
Assuming that no heat is lost to the surroundings calculate the specific heat of nickel.
[mass Ni x specific heat Ni x (Tfinal-Tinitial)] + [mass H2O x specific heat H2O x (Tfinal-Tinitial)] + Ccal x (Tfinal-Tinitial) = 0
specific heat Ni is the only unknown. Substitute and solve for that. Post your work if you get stuck.
To calculate the specific heat of nickel, we can use the principle of conservation of energy, which states that the heat gained by the water and the calorimeter is equal to the heat lost by the nickel.
First, let's calculate the heat gained by the water and the calorimeter using the equation:
Q_water_calorimeter = (mass_water_calorimeter + mass_water) * specific_heat_water * ΔT
Where:
mass_water_calorimeter = mass of water in the calorimeter
mass_water = mass of water added to the calorimeter
specific_heat_water = specific heat capacity of water
ΔT = change in temperature (final temperature - initial temperature)
mass_water_calorimeter = 81.11 grams
mass_water = 0 grams (as no additional water is added)
specific_heat_water = 4.18 J/g°C (specific heat capacity of water)
ΔT = 27.84 °C - 21.79 °C
Q_water_calorimeter = (81.11 g + 0 g) * 4.18 J/g°C * (27.84 °C - 21.79 °C)
Q_water_calorimeter = 81.11 g * 4.18 J/g°C * 6.05 °C
Q_water_calorimeter = 2018.763 J
Next, we need to calculate the heat lost by the nickel using the equation:
Q_nickel = mass_nickel * specific_heat_nickel * ΔT
Where:
mass_nickel = mass of the nickel
specific_heat_nickel = specific heat capacity of nickel
ΔT = change in temperature (final temperature - initial temperature)
mass_nickel = 64.05 grams
specific_heat_nickel = ? (we need to calculate this)
ΔT = 27.84 °C - 97.80 °C
Q_nickel = 64.05 g * specific_heat_nickel * (-69.96 °C)
Q_nickel = -4483.079 g°C * specific_heat_nickel
Since the heat lost by the nickel is equal to the heat gained by the water and the calorimeter, we can set up the equation:
Q_water_calorimeter = Q_nickel
2018.763 J = -4483.079 g°C * specific_heat_nickel
Now, let's solve for the specific heat of nickel:
specific_heat_nickel = 2018.763 J / (-4483.079 g°C)
specific_heat_nickel = -0.449 J/g°C
Therefore, the specific heat of nickel is -0.449 J/g°C.
To calculate the specific heat of nickel, we need to use the principle of energy conservation. In this scenario, the heat gained by the water is equal to the heat lost by the nickel.
First, we need to calculate the heat gained by the water using the formula:
Qwater = mass_water * specific_heat_water * change_in_temperature_water
where:
mass_water is the mass of water
specific_heat_water is the specific heat capacity of water
change_in_temperature_water is the change in temperature of water
mass_water = 81.11 grams
specific_heat_water = 4.18 J/g°C (specific heat capacity of water)
change_in_temperature_water = final_temperature_water - initial_temperature_water
Since the final temperature of the water is given as 27.84 °C, the initial temperature of the water must be 21.79 °C.
change_in_temperature_water = 27.84 °C - 21.79 °C = 6.05 °C
Now we can calculate the heat gained by the water:
Qwater = 81.11 g * 4.18 J/g°C * 6.05 °C
Next, we need to calculate the heat lost by the nickel using the formula:
Qnickel = mass_nickel * specific_heat_nickel * change_in_temperature_nickel
where:
mass_nickel is the mass of nickel
specific_heat_nickel is the specific heat capacity of nickel
change_in_temperature_nickel is the change in temperature of nickel
mass_nickel = 64.05 grams
change_in_temperature_nickel = final_temperature_nickel - initial_temperature_nickel
Since the final temperature of the nickel is given as 27.84 °C, the initial temperature of the nickel must be 97.80 °C.
change_in_temperature_nickel = 27.84 °C - 97.80 °C = -69.96 °C
(Note: The change in temperature is negative because the nickel is cooling down.)
Now we can calculate the heat lost by the nickel:
Qnickel = 64.05 g * specific_heat_nickel * -69.96 °C
Since the heat lost by the nickel is equal to the heat gained by the water, we can set up an equation and solve for the specific heat of nickel:
Qnickel = Qwater
64.05 g * specific_heat_nickel * -69.96 °C = 81.11 g * 4.18 J/g°C * 6.05 °C
Rewriting the equation:
specific_heat_nickel = (81.11 g * 4.18 J/g°C * 6.05 °C) / (64.05 g * -69.96 °C)
Now we can calculate the specific heat of nickel.