If 0.045 kg of ice at 0 C is added to 0.390 kg of water at 34 C in a 0.150 kg aluminum calorimeter cup, what is the final temperature of the water? If the final equilibrium temperature is 21 C and no heat is lost to the cup itself or the environment, what is the mass of the aluminum spoon?
To find the final temperature of the water, we can use the principle of conservation of energy. The heat gained by the water and the cup must equal the heat lost by the ice.
First, let's find the heat gained by the water:
Heat gained = mass of water * specific heat capacity of water * change in temperature
The mass of water is given as 0.390 kg, the specific heat capacity of water is approximately 4186 J/kg⋅°C, and the change in temperature is the final temperature (Tf) minus the initial temperature (Ti), which is 21°C - 34°C = -13°C.
Heat gained by water = 0.390 kg * 4186 J/kg⋅°C * (-13°C)
Next, let's find the heat lost by the ice:
Heat lost = mass of ice * specific heat capacity of ice * change in temperature
The mass of ice is given as 0.045 kg, the specific heat capacity of ice is approximately 2090 J/kg⋅°C, and the change in temperature is the final temperature (Tf) minus the initial temperature (Ti), which is 0°C - 21°C = -21°C.
Heat lost by ice = 0.045 kg * 2090 J/kg⋅°C * (-21°C)
Now, since no heat is lost to the cup or the environment, the heat gained by the water and the cup must equal the heat lost by the ice. Therefore, we can set up the equation:
Heat gained by water = Heat lost by ice
0.390 kg * 4186 J/kg⋅°C * (-13°C) = 0.045 kg * 2090 J/kg⋅°C * (-21°C)
Simplifying the equation, we get:
-53478 J = -19845 J
Since the left side and right side of the equation are equal, we know that the equation is balanced.
Now, let's calculate the mass of the aluminum spoon. Since the spoon does not gain or lose any heat, we can use the same principle of conservation of energy:
Heat gained by the spoon = Heat lost by the water
From the previous calculations, we know that the heat gained by the water is -53478 J. The specific heat capacity of aluminum is approximately 900 J/kg⋅°C, and the change in temperature is the final temperature (21°C) minus the initial temperature (34°C), which is -13°C.
Heat gained by spoon = mass of spoon * specific heat capacity of aluminum * change in temperature
-53478 J = mass of spoon * 900 J/kg⋅°C * (-13°C)
Simplifying the equation, we get:
mass of spoon = -53478 J / (900 J/kg⋅°C * (-13°C))
mass of spoon ≈ 4.03 kg
Therefore, the mass of the aluminum spoon is approximately 4.03 kg.