To find the final temperature when the two samples of water are mixed, we can use the principle of conservation of energy. The heat lost by the hot water (initially at 100°C) will be equal to the heat gained by the cold water (initially at 25°C).
The heat gained or lost by a substance can be calculated using the formula:
Q = mcΔT
Where:
- Q is the heat gained or lost
- m is the mass of the substance
- c is the specific heat capacity of the substance
- ΔT is the change in temperature
For the hot water:
Q_hot = m_hot * c * ΔT_hot
For the cold water:
Q_cold = m_cold * c * ΔT_cold
Since the total heat lost by the hot water equals the total heat gained by the cold water, we have:
Q_hot = -Q_cold
Now, we can plug in the given values and solve for the final temperature:
Q_hot = -Q_cold
m_hot * c * ΔT_hot = -m_cold * c * ΔT_cold
Let's calculate each term:
m_hot = 56.0 g
m_cold = 46.0 g
c = 4.184 J/g°C
For the hot water:
ΔT_hot = T_final - 100°C
For the cold water:
ΔT_cold = T_final - 25°C
Now, we can rewrite the equation:
56.0 g * 4.184 J/g°C * (T_final - 100°C) = -46.0 g * 4.184 J/g°C * (T_final - 25°C)
Now, we can solve for T_final:
56.0 * 4.184 * (T_final - 100) = -46.0 * 4.184 * (T_final - 25)
235.136 * T_final - 23513.6 = -193.184 * T_final + 4829
Combine like terms:
428.32 * T_final = 28342.6
T_final = 28342.6 / 428.32
T_final ≈ 66.22°C
Therefore, the final temperature of the water will be approximately 66.22°C.
