550 g of water (cw = 4186 J/kg.K) at 75°C is poured into an 855 g aluminum (cw =900 J/kg.K) container with an initial temperature of 11°C. What is the final temperature of the system, assuming no heat is exchanged with the surroundings?
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heat lost by water + heat gained by Al = 0
[mass H2O x specific heat H2O x (Tfinal - Tinitial)] + [mass Al x specific heat Al x (Final-Tinitial)] = 0
Substitute and solve for Tf.
To answer this question, we can use the principle of conservation of energy. We know that the heat gained by the water is equal to the heat lost by the aluminum container.
The equation to calculate the heat gained or lost is:
Q = mcΔT
Where:
Q is the heat gained or lost (in joules)
m is the mass of the substance (in kilograms)
c is the specific heat capacity of the substance (in J/kg.K)
ΔT is the change in temperature (in kelvin)
First, let's calculate the heat gained by the water:
Q_water = mw * cw * ΔTw
Where:
mw is the mass of the water (550 g = 0.55 kg)
cw is the specific heat capacity of water (4186 J/kg.K)
ΔTw is the change in temperature of the water (final temperature - initial temperature)
Substituting the known values:
Q_water = 0.55 * 4186 * (Tf - 75)
Next, let's calculate the heat lost by the aluminum container:
Q_aluminum = ma * ca * ΔTa
Where:
ma is the mass of the aluminum container (855 g = 0.855 kg)
ca is the specific heat capacity of aluminum (900 J/kg.K)
ΔTa is the change in temperature of the aluminum (final temperature - initial temperature)
Substituting the known values:
Q_aluminum = 0.855 * 900 * (Tf - 11)
According to the principle of conservation of energy, when there is no heat exchange with the surroundings, the heat gained by the water is equal to the heat lost by the aluminum container:
Q_water = Q_aluminum
0.55 * 4186 * (Tf - 75) = 0.855 * 900 * (Tf - 11)
Now, we can solve this equation to find the final temperature (Tf) of the system.