A 25kg copper at 100c is placed in a container of water. the water has a mass of 45kg and it is at 45c beffore the copper was added. what is the final temperature of the mixture?
[mass Cu x specific heat Cu x (Tfinal-Tinitial)] + [mass H2O x specific heat H2O x (Tfinal - Tinitial)] = 0
Substitute the following from the porblem:
mass Cu = 25,000 g
specific heat Cu = Look this up in your text/notes/web and make sure the units are J/g*C.
Tfinal Cu = unknown. Solve for this.
Tinitial Cu = 100 celsius from the problem.
mass H2O = 45.000 g from the problem.
specific heat H2O = I remember this as 4.18 J/g*C
Tinitial H2O = 45 celsius from the problem.
Tfinal H2O = this is the unknown and is the same as Tfinal Cu. So I would substitute x for each of these and solve for x. Post your work if you get stuck.
heat lost by copper is gained by water
25 kg * (100 - t) * (s.h. Cu) = 45 kg * (t - 45) * (s.h. H2O)
s.h. Cu is ... 385 J/kg⋅ºC
s.h. H2O is ... 4184 J/kg⋅ºC
To find the final temperature of the mixture, we can use the principle of conservation of energy. The energy gained by the cold water and copper will be equal to the energy lost by the hot water and copper.
First, we need to calculate the energy gained or lost by the water and copper using the specific heat capacity formula:
Energy gained or lost = mass × specific heat capacity × change in temperature
The specific heat capacity of copper is approximately 387 J/kg°C, while the specific heat capacity of water is approximately 4186 J/kg°C.
For the water:
Energy gained or lost by the water = 45 kg × 4186 J/kg°C × (final temperature - initial temperature)
For the copper:
Energy gained or lost by the copper = 25 kg × 387 J/kg°C × (final temperature - initial temperature)
Since the energy gained by the cold water and copper is equal to the energy lost by the hot water and copper, we can set up the equation:
(45 kg × 4186 J/kg°C × (final temperature - 45°C)) + (25 kg × 387 J/kg°C × (final temperature - 100°C)) = 0
Now we can solve this equation to find the final temperature of the mixture.