An aluminum calorimeter of mass 400g contains 200g of water at a temperature of 18celcius.When a block of nickel at a temperature of 80celcius is dropped into the water£¬the final temperature of the mixture becomes 28celcius. Find the mass of the nickel.
The sum of heats gained is zero. Heat gained=mcDeltaT
400*calum*(28-18)+200*cwater*(28-18)+MassNi*Cni*(28-80)=0
solve for MassNi
To find the mass of the nickel block, we can use the principles of heat transfer and calorimetry. The heat gained by the water and the calorimeter is equal to the heat lost by the nickel block.
First, let's determine the heat gained by the water and the calorimeter. We can use the formula:
Q = mcΔt
Where:
Q = Heat gained or lost
m = Mass
c = Specific heat capacity
Δt = Change in temperature
The specific heat capacity of water is approximately 4.18 J/g°C, and the specific heat capacity of aluminum is approximately 0.9 J/g°C.
For the water and calorimeter:
Qwater_calorimeter = (mass of water + mass of calorimeter) * specific heat capacity * Δt
Qwater_calorimeter = (200g + 400g) * 4.18 J/g°C * (28°C - 18°C)
Qwater_calorimeter = 600g * 4.18 J/g°C * 10°C
Qwater_calorimeter = 25,080 J
Now, let's determine the heat lost by the nickel block. We can use the same formula:
Qnickel = mass of nickel * specific heat capacity * Δt
Qnickel = mass of nickel * specific heat capacity * (initial temperature - final temperature)
Qnickel = mass of nickel * specific heat capacity * (80°C - 28°C)
Qnickel = mass of nickel * specific heat capacity * 52°C
Next, since the heat gained by the water and calorimeter is equal to the heat lost by the nickel block, we can set up the equation:
Qwater_calorimeter = Qnickel
25,080 J = mass of nickel * specific heat capacity * 52°C
To find the mass of the nickel, rearrange the equation:
Mass of nickel = 25,080 J / (specific heat capacity * 52°C)
Since the specific heat capacity of nickel is typically around 0.44 J/g°C, we can substitute the value into the equation:
Mass of nickel = 25,080 J / (0.44 J/g°C * 52°C)
Mass of nickel = 1,137.27 g
Therefore, the mass of the nickel block is approximately 1,137.27 grams.