A piece of aluminum with an unknown mass ios at 85c and is placed in a 2.00 liters of water at 25.0c. The final temperature becomes 33c. What is the mass of aluminum?
To find the mass of the aluminum, we can use the principle of heat transfer known as the heat equation:
Q = mcΔT
Where:
Q represents the heat transferred,
m represents the mass of the object,
c represents the specific heat capacity, and
ΔT represents the change in temperature.
In this case, the heat transferred between the aluminum and the water can be determined using the formula:
Q = Q(aluminum) = Q(water)
Assuming there is no heat lost to the surroundings, we can write:
mcΔT(aluminum) = mcΔT(water)
Since we are trying to find the mass of aluminum, we can rearrange the equation:
m(aluminum) = (mcΔT(water)) / (c(aluminum)ΔT(aluminum))
Given that the specific heat capacity of water is approximately 4.18 J/g°C and that of aluminum is 0.90 J/g°C, and substituting the values into the equation, we have:
m(aluminum) = (2.00 L x 4.18 J/g°C x (33°C - 25°C)) / (0.90 J/g°C x (33°C - 85°C))
Simplifying the equation:
m(aluminum) = (2.00 L x 4.18 J/g°C x 8°C) / (0.90 J/g°C x -52°C)
The volume of water should be converted to grams since specific heat capacity is typically given in terms of grams. We know that 1 g of water occupies 1 mL, so we can say that 1 L of water weighs 1000 g. If we multiply the volume by the density, we get the mass:
m(aluminum) = (2000 g x 4.18 J/g°C x 8°C) / (0.90 J/g°C x -52°C)
Calculating the values:
m(aluminum) = -332.8 g / -46.8 g
m(aluminum) ≈ 7.1 g
Therefore, the mass of the aluminum is approximately 7.1 grams.