An aluminum calorimeter has a mass of 60g and an initial temperature of 25oC. What is the final temperature attained when 86.8g of water at 90oC is poured into it?
The sum of the heats gained is zero.
heatgainedwater+heatgainedAl=0
86.8*cwater*( Tf-90 )+60*calum*(Tf-25)=0
Ok, but then how do you find Tf?
To find the final temperature attained when water is poured into the aluminum calorimeter, we can use the principle of heat transfer. The heat gained by the water will be equal to the heat lost by the calorimeter.
First, let's calculate the heat gained by the water using the formula:
Q = mcΔT
Where:
Q is the heat gained or lost
m is the mass of the water
c is the specific heat capacity of water
ΔT is the change in temperature
The specific heat capacity of water is typically 4.18 J/g°C.
Given:
m = 86.8g (mass of water)
ΔT = (final temperature of water) - initial temperature of water = (final temperature of water) - 90°C
Now we can calculate the heat gained by the water:
Q_water = mcΔT = 86.8g * 4.18 J/g°C * ((final temperature of water) - 90°C)
Now let's calculate the heat lost by the calorimeter.
Q_calorimeter = mcΔT = 60g * specific heat capacity of aluminum * (final temperature of calorimeter - initial temperature of calorimeter)
Since the specific heat capacity of aluminum is typically 0.897 J/g°C, we have:
Q_calorimeter = 60g * 0.897 J/g°C * ((final temperature of calorimeter) - 25°C)
According to the principle of heat transfer, the heat gained by the water is equal to the heat lost by the calorimeter. Therefore, we have:
Q_water = Q_calorimeter
Combine the equations and set them equal to each other:
86.8g * 4.18 J/g°C * ((final temperature of water) - 90°C) = 60g * 0.897 J/g°C * ((final temperature of calorimeter) - 25°C)
Now we can solve for the final temperature of the water by rearranging the equation and isolating the variable:
(final temperature of water) - 90°C = (60g * 0.897 J/g°C * ((final temperature of calorimeter) - 25°C))/(86.8g * 4.18 J/g°C)
(final temperature of water) = 90°C + (60g * 0.897 J/g°C * ((final temperature of calorimeter) - 25°C))/(86.8g * 4.18 J/g°C)
Now you can substitute the given values and solve for the final temperature of the water.