A 275-g. sample of nickel at 100 degrees C is placed in 100 g. of water at 22 degrees C. What is the final temperature of water? Assume that no energy is gained or lost to the calorimeter or the surroundings. Specific heat capacity of nickel = .444 J/ (g*k).
thanks dr. bob!
To calculate the final temperature of water after adding the nickel sample, we will use the principle of energy conservation.
The amount of heat gained by the water (Qwater) should be equal to the amount of heat lost by the nickel (Qnickel). The equation for heat is given by:
Q = mcΔT
Where:
Q represents the heat absorbed or released
m is the mass of the substance
c is the specific heat capacity of the substance
ΔT is the change in temperature
Let's calculate the heat gained by the water:
Qwater = mcΔT
mwater = 100 g
cwater = 4.184 J/(g·°C) (specific heat capacity of water)
Tfinal_water = ?
Tinitial_water = 22 °C
Qwater = (100 g) * (4.184 J/(g·°C)) * (Tfinal_water - 22 °C)
Now, let's calculate the heat lost by the nickel:
Qnickel = mcΔT
mnickel = 275 g
cnickel = 0.444 J/(g·°C) (specific heat capacity of nickel)
Tinitial_nickel = 100 °C
Tfinal_nickel = ?
Qnickel = (275 g) * (0.444 J/(g·°C)) * (100 °C - Tfinal_nickel)
Since the heat gained by the water is equal to the heat lost by the nickel:
Qwater = Qnickel
(100 g) * (4.184 J/(g·°C)) * (Tfinal_water - 22 °C) = (275 g) * (0.444 J/(g·°C)) * (100 °C - Tfinal_nickel)
Now we can solve this equation to find the final temperature of the water (Tfinal_water).
Please note that without additional information, it is difficult to solve for the final temperature precisely.
To calculate the final temperature of water after the nickel sample is added, we can use the principle of conservation of energy. The energy lost by the nickel will be equal to the energy gained by the water.
First, let's calculate the energy lost by the nickel sample. We can use the formula:
Energy lost by nickel = mass of nickel * specific heat capacity of nickel * change in temperature
The mass of nickel is given as 275 g and the specific heat capacity of nickel is 0.444 J/ (g*k). The change in temperature is the final temperature (Tf) minus the initial temperature (Ti).
Since no energy is gained or lost to the surroundings, the energy lost by the nickel is equal to the energy gained by the water. We can use the same formula to calculate the energy gained by the water:
Energy gained by water = mass of water * specific heat capacity of water * change in temperature
In this case, the mass of water is given as 100 g. The specific heat capacity of water is typically around 4.18 J/ (g*k) but it is not specified in the question. Assuming it is the same as the specific heat capacity of liquid water, we can use this value.
Since the energy lost by the nickel is equal to the energy gained by the water, we can set these two equations equal to each other:
mass of nickel * specific heat capacity of nickel * (Tf - Ti) = mass of water * specific heat capacity of water * (Tf - Ti)
Substituting the given values, we have:
275 g * 0.444 J/ (g*k) * (Tf - 100°C) = 100 g * 4.18 J/ (g*k) * (Tf - 22°C)
Now we can solve for Tf, the final temperature of the water. Rearranging the equation, we get:
275 * 0.444 * (Tf - 100) = 100 * 4.18 * (Tf - 22)
Simplifying further:
122.1 * (Tf - 100) = 418 * (Tf - 22)
Distributing and combining like terms:
122.1Tf - 12210 = 418Tf - 9220
Collecting the terms with Tf on one side of the equation:
122.1Tf - 418Tf = -9220 + 12210
-295.9Tf = 2990
Dividing by -295.9:
Tf = 2990 / -295.9
Tf ≈ -10.10°C
Therefore, the final temperature of the water is approximately -10.10°C.
Heat lost by nickel + heat gained by water = 0
[mass Ni x specific heat Ni x (Tfinal-Tinitial)] + [mass H2O x specific heat H2O x (Tfinal-Tinitial)] = 0