Applying the principle of conservation of energy, the final temperature after mixing 225 mL of water at 25°C with 85 mL of water at 89°C is approximately 42.60°C.
To find the final temperature when two substances at different temperatures are mixed, you can use the principle of conservation of energy, which states that the heat lost by the hot substance is equal to the heat gained by the cold substance.
The formula for heat transfer (Q) is given by:
Q = mcΔT
Where:
Q is the heat transfer,
m is the mass of the substance,
c is the specific heat of the substance,
ΔT is the change in temperature.
Let's denote the initial temperature of the cold water as T_c, the initial temperature of the hot water as T_h, the final temperature as T_f, the mass of the cold water as mc, and the mass of the hot water as mh.
The heat lost by the hot water is equal to the heat gained by the cold water:
mh c (T_h - T_f) = mc c (T_f - T_c)
Given that the density of water is 1.00 g/mL, we can use the formula mass = density × volume to express the masses in terms of volumes:
mh = 85 mL × 1.00 g/mL
mc = 225 mL × 1.00 g/mL
Substitute these values into the heat transfer equation:
85 mL × 1.00 g/mL × 4.184 J/g°C × (89°C - T_f) = 225 mL × 1.00 g/mL × 4.184 J/g°C × (T_f - 25°C)
Now, solve for T_f:
85 g × 4.184 J/g°C × (89°C - T_f) = 225 g × 4.184 J/g°C × (T_f - 25°C)
355.24 (89 - T_f) = 940.4 (T_f - 25)
Now, solve for T_f:
355.24 × 89 - 355.24 × T_f = 940.4 × T_f - 940.4 × 25
31551.36 - 355.24 × T_f = 940.4 × T_f - 23510
1290.64 × T_f = 55041.36
T_f = 55041.36 / 1290.64
T_f ≈ 42.60°C
Therefore, the final temperature is approximately 42.60°C.