A 33.0g sample of aluminum, which has a specific heat capacity of 0.897·J·g−1°C−1, is dropped into an insulated container containing 250.0g of water at 25.0°C and a constant pressure of 1atm. The initial temperature of the aluminum is 83.2°C.Assuming no heat is absorbed from or by the container, or the surroundings, calculate the equilibrium temperature of the water. Be sure your answer has the correct number of significant digits.°C
Question
A 33.0g sample of aluminum, which has a specific heat capacity of 0.897·J·g−1°C−1, is dropped into an insulated container containing 250.0g of water at 25.0°C and a constant pressure of 1atm. The initial temperature of the aluminum is 83.2°C.Assuming no heat is absorbed from or by the container, or the surroundings, calculate the equilibrium temperature of the water. Be sure your answer has the correct number of significant digits.°C
Solution
To solve this problem, we need to use the principle of conservation of energy, which states that energy cannot be created or destroyed, only transferred. In this case, the heat lost by the aluminum will be equal to the heat gained by the water.
The formula for heat transfer is Q = mcΔT, where Q is the heat transferred, m is the mass, c is the specific heat capacity, and ΔT is the change in temperature.
First, we calculate the heat lost by the aluminum:
Q_Al = m_Al * c_Al * (T_initial_Al - T_final)
We don't know the final temperature of the aluminum yet, but we can express it as T_final.
Next, we calculate the heat gained by the water:
Q_Water = m_Water * c_Water * (T_final - T_initial_Water)
The specific heat capacity of water is 4.184 J/g°C.
Since the heat lost by the aluminum is equal to the heat gained by the water, we can set the two equations equal to each other and solve for T_final:
m_Al * c_Al * (T_initial_Al - T_final) = m_Water * c_Water * (T_final - T_initial_Water)
Substituting the given values:
33.0g * 0.897 J/g°C * (83.2°C - T_final) = 250.0g * 4.184 J/g°C * (T_final - 25.0°C)
Solving this equation for T_final gives the equilibrium temperature of the water.
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