If 100.0 g of water at 90'C is added to 50.0 g of water at 10'C, estimate the final temperature of the water. explain your reasoning.
please my last question i really don't get it, :/
heat gained by cool water + heat lost by warm water = 0
[mass cool H2O x specific heat x (Tfinal-Tinitial)] + [mass warm H2O x specific heat x (Tfinal-Tinitial)] = 0
Substitute and solve for Tfinal.
If 100.0 g of water at 90 ° C is added to 50.0 g of water at 10 ° C, estimate the final temperature of the water and explain your reasoning.
To estimate the final temperature of the water when 100.0 g of water at 90°C is added to 50.0 g of water at 10°C, we can use the principle of energy conservation.
Here's how we can approach the problem step-by-step:
1. Calculate the heat gain of the cold water (50.0 g at 10°C).
- The specific heat capacity of water is approximately 4.18 J/g°C.
- The heat gain is given by the formula: Q = mcΔT, where Q is the heat gain, m is the mass of the water, c is the specific heat capacity, and ΔT is the change in temperature.
- Substituting the values: Q = 50.0 g × 4.18 J/g°C × [final temperature - 10°C] (Note: final temperature is unknown at this point).
2. Calculate the heat loss of the hot water (100.0 g at 90°C).
- Again, Q = mcΔT, but this time the temperature change is final temperature - 90°C.
- Substituting the values: Q = 100.0 g × 4.18 J/g°C × [final temperature - 90°C].
3. Apply the principle of energy conservation.
- According to the law of energy conservation, the heat gained by the cold water is equal to the heat lost by the hot water when they mix, assuming no heat is lost to the surroundings.
- Set up an equation: heat gain of cold water = heat loss of hot water.
- This gives us: 50.0 g × 4.18 J/g°C × [final temperature - 10°C] = 100.0 g × 4.18 J/g°C × [final temperature - 90°C].
- Solve this equation for the final temperature.
By solving the equation, you will find the estimated final temperature of the water when the two masses are mixed together.
To estimate the final temperature of the water, we can use the principle of conservation of energy. When the hot water is mixed with the cold water, heat will be transferred from the hot water to the cold water until they reach a common final temperature.
To calculate the final temperature, we can use the equation:
(m1 * c1 * ΔT1) + (m2 * c2 * ΔT2) = 0
Where:
m1 is the mass of the hot water (100.0 g)
c1 is the specific heat capacity of water
ΔT1 is the change in temperature of the hot water (final temperature - initial temperature)
m2 is the mass of the cold water (50.0 g)
c2 is the specific heat capacity of water
ΔT2 is the change in temperature of the cold water (final temperature - initial temperature)
The specific heat capacity of water is approximately 4.18 J/g°C.
Let's substitute the known values into the equation:
(100.0 g * 4.18 J/g°C * (Tf - 90°C)) + (50.0 g * 4.18 J/g°C * (Tf - 10°C)) = 0
Now, we can solve this equation to find the final temperature (Tf).
First, distribute the multiplication:
(418 g°C * Tf - 37620 J) + (209 g°C * Tf - 1045 J) = 0
Combine like terms:
627 g°C * Tf - 38665 J = 0
Now, isolate Tf by moving the constant term to the other side:
627 g°C * Tf = 38665 J
Divide both sides by 627 g°C:
Tf = 38665 J / 627 g°C
Tf ≈ 61.7°C
Therefore, the estimated final temperature of the water will be approximately 61.7°C.