If 50.0grams of copper initially at 145.0 C is put into 150.0mL of water initially at 25.00C, then what will the final temperature of the mixture be? assume that all of the heat lost by the hot copper is absorbed by the cold water.
heat lost by Cu + heat gained by H2O = 0.
[(mass Cu x specific heat Cu x (Tfinal-Tinitial)] + [(mass H2O x specific heat H2O x (Tfinal-Tinitial)] = 0
To find the final temperature of the mixture, we need to apply the principle of heat exchange, specifically using the equation:
(heat lost by copper) = (heat gained by water)
This equation is based on the principle of conservation of energy, which states that energy cannot be created or destroyed, only transferred or converted from one form to another.
First, we need to calculate the heat lost by the copper. To do this, we'll use the specific heat capacity formula:
Q = m * c * ΔT
Where:
Q = heat
m = mass
c = specific heat capacity
ΔT = change in temperature
The specific heat capacity of copper is 0.385 J/g°C, and the mass of copper is given as 50.0 grams. The initial temperature of the copper is 145.0°C, and the final temperature is unknown. So the equation becomes:
Q(copper) = (50.0 g) * (0.385 J/g°C) * (145.0°C - final temperature)
Next, we calculate the heat gained by water using the same formula. The specific heat capacity of water is 4.18 J/g°C, and the mass of water is given as 150.0 mL. However, we need to convert mL to grams to use the formula. The density of water is 1 g/mL, so the mass of water becomes:
mass of water = 150.0 mL * 1 g/mL = 150.0 g
The initial temperature of the water is 25.00°C, and the final temperature is unknown. The equation becomes:
Q(water) = (150.0 g) * (4.18 J/g°C) * (final temperature - 25.00°C)
Since the heat lost by the copper is equal to the heat gained by the water, we can set up the following equation:
Q(copper) = Q(water)
(50.0 g) * (0.385 J/g°C) * (145.0°C - final temperature) = (150.0 g) * (4.18 J/g°C) * (final temperature - 25.00°C)
Now, we can solve this equation for the final temperature of the mixture.