Mix 25 ml of water at 0 degrees Celsius
and 25 ml of water at 50 degrees Celsius. What is the final temperature of the water?
The average of the two, since the amounts are equal.
To find the final temperature of the water, we can use the principle of conservation of energy.
The equation for heat transfer is:
Q = mcΔT
Where:
Q = heat transferred
m = mass of the substance (in this case, water)
c = specific heat capacity of the substance (for water, it is approximately 4.18 J/g°C)
ΔT = change in temperature
First, let's calculate the heat transferred when the cold water warms up:
Q1 = m1 * c * ΔT1
Where:
m1 = mass of water at 0 degrees Celsius (25 ml = 25 g)
c = specific heat capacity of water (4.18 J/g°C)
ΔT1 = final temperature - initial temperature = Tf - 0°C
Next, let's calculate the heat transferred when the hot water cools down:
Q2 = m2 * c * ΔT2
Where:
m2 = mass of water at 50 degrees Celsius (25 ml = 25 g)
c = specific heat capacity of water (4.18 J/g°C)
ΔT2 = initial temperature - final temperature = 50°C - Tf
According to the principle of energy conservation, the amount of heat lost by the hot water (Q2) should be equal to the amount of heat gained by the cold water (Q1):
Q1 = Q2
m1 * c * ΔT1 = m2 * c * ΔT2
Now, we can substitute the given values:
25 g * 4.18 J/g°C * (Tf - 0°C) = 25 g * 4.18 J/g°C * (50°C - Tf)
Simplifying the equation:
104.5 Tf = 104.5 * 50
Tf = 50
Therefore, the final temperature of the water is 50 degrees Celsius.