pour a liter of water at 40 c into a liter of water at 20 and the final temperature of the two becomes about____________________c
With equal masses, you end up with the average temperature of the two, 30 C
To find the final temperature of a mixture, we can use the principle of conservation of energy, which states that the total energy of the system remains constant.
First, we need to determine the amount of heat exchanged between the two water samples. We can use the formula:
Q = mcΔT
where Q represents the heat transferred, m represents the mass, c represents the specific heat capacity, and ΔT represents the change in temperature.
Let's assume that both water samples have a mass of 1 kg (since density of water is approximately 1 g/cm³).
The specific heat capacity of water is approximately 4.18 J/(g·°C) or 4.18 kJ/(kg·°C).
For the first water sample at 40 °C:
Q1 = (1 kg) × (4.18 kJ/(kg·°C)) × (40 °C - TF)
For the second water sample at 20 °C:
Q2 = (1 kg) × (4.18 kJ/(kg·°C)) × (TF - 20 °C)
Since energy is conserved, Q1 = -Q2 (as heat flows from the hotter to the cooler region). Thus, we can equate the two equations:
(1 kg) × (4.18 kJ/(kg·°C)) × (40 °C - TF) = (1 kg) × (4.18 kJ/(kg·°C)) × (TF - 20 °C)
Next, we can solve the equation for TF (the final temperature):
(40 °C - TF) = (TF - 20 °C)
40 °C - TF = TF - 20 °C
Combining like terms:
20 °C = 2TF
Dividing by 2:
TF = 10 °C
Therefore, the final temperature of the water mixture will be approximately 10 °C.
To determine the final temperature of the two liters of water when mixed together, we can use the principle of conservation of energy and the specific heat capacity of water.
The principle of conservation of energy states that the total energy of a closed system remains constant. When the two liters of water are mixed together, the energy gained by one liter (initially at 40°C) will be equal to the energy lost by the other liter (initially at 20°C).
To calculate this, we need to use the equation:
Q = mcΔT
Where:
Q = heat energy (in joules)
m = mass of the water (liters)
c = specific heat capacity of water (approx. 4.186 J/g°C)
Since we have one liter of water on both sides, the mass cancels out, and the equation becomes:
Q1 = Q2
m1cΔT1 = m2cΔT2
Substituting the known values:
1 * 4.186 * (40 - T) = 1 * 4.186 * (T - 20)
Simplifying the equation further:
4.186 * (40 - T) = 4.186 * (T - 20)
Now we can solve the equation to find the final temperature, T.
4.186 * 40 - 4.186T = 4.186T - 4.186 * 20
167.44 - 4.186T = 4.186T - 83.72
Combining like terms:
-4.186T - 4.186T = -83.72 - 167.44
-8.372T = -251.16
Dividing both sides of the equation by -8.372:
T = -251.16 / -8.372
T ≈ 30°C
Therefore, the final temperature of the two liters of water after being mixed will be approximately 30°C.