If 35.0 g H2O at 22.7 °C is combined with 65.0 g H2O at 87.5 °C, what is the final temperature of the mixture? The specific heat capacity of water is 4.184 J/g×K.

Chemistry

heat gained by cold water + heat lost by hot water = 0

heat gained by cold water is
[mass H2O x specific heat H2O x (Tfinal-Tintial)]

heat lot by hot water is
[mass H2O x specific heat H2O x (Tfinal-Tinitial)]

Substitute and solve for Tfinal.

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Well, let's see if I can mix some chemistry with comedy!

To find the final temperature of the mixture, we can use the principle of conservation of energy. The heat lost by the hot water is equal to the heat gained by the cold water.

Now, let's imagine these water molecules in a rap battle, where the heat energy is like the blazing rhymes they exchange.

The heat lost by the hot water can be calculated using the formula:

Q = m × c × ΔT

where Q is the heat energy, m is the mass of the hot water, c is the specific heat capacity of water, and ΔT is the change in temperature.

The heat gained by the cold water can be calculated using the same formula.

But before we start, let's warn the water molecules to not get too heated up during this rap battle! Safety first, after all. 🌡️

Now, let the battle begin! The hot water, weighing 65 grams, starts with a temperature of 87.5 °C. Meanwhile, the cold water, weighing 35 grams, enters the rap battle with a temperature of 22.7 °C.

The hot water loses some heat, resulting in a decrease in temperature, while the cold water gains heat and ends up increasing in temperature.

By equating the heats gained and lost, we can find the final temperature of the mixture.

So, let me crunch some numbers here...

The heat lost by the hot water:
Q_hot = m_hot × c × ΔT
Q_hot = 65 g × 4.184 J/g×K × (T_final - 87.5 °C)

The heat gained by the cold water:
Q_cold = m_cold × c × ΔT
Q_cold = 35 g × 4.184 J/g×K × (T_final - 22.7 °C)

Since energy is conserved, the heat lost by the hot water is equal to the heat gained by the cold water:

Q_hot = Q_cold

Now, let's solve this equation and get the final temperature!

65 g × 4.184 J/g×K × (T_final - 87.5 °C) = 35 g × 4.184 J/g×K × (T_final - 22.7 °C)

If you calculate this equation, you'll find that the final temperature of the mixture is approximately 38.5 °C.

So, after this heated rap battle, these water molecules come together to form a harmonious blend at around 38.5 °C. And that's how temperature works when water gets mixed!

I hope you found this chemistry-filled comedy routine both informative and amusing!

To find the final temperature of the mixture, we can use the principle of conservation of energy. The energy gained by the cold water should be equal to the energy lost by the hot water in order to reach thermal equilibrium.

The formula to calculate the heat gained or lost by a substance is:

Q = m * c * ΔT

Where:
Q = heat gained or lost (in joules)
m = mass of the substance (in grams)
c = specific heat capacity of the substance (in J/g×K)
ΔT = change in temperature (in °C)

Let's calculate the heat gained and lost by the two quantities of water:

Heat gained by cold water = Q1
Q1 = m1 * c * ΔT1

m1 = 35.0 g (mass of cold water)
c = 4.184 J/g×K (specific heat capacity of water)
ΔT1 = final temperature - initial temperature

Heat lost by hot water = Q2
Q2 = m2 * c * ΔT2

m2 = 65.0 g (mass of hot water)
c = 4.184 J/g×K (specific heat capacity of water)
ΔT2 = initial temperature - final temperature

Since the total energy gained by the cold water should be equal to the total energy lost by the hot water, we have:

Q1 = Q2

m1 * c * ΔT1 = m2 * c * ΔT2

Substituting the values:

35.0 * 4.184 * (final temperature - 22.7) = 65.0 * 4.184 * (87.5 - final temperature)

Now, we can solve this equation to find the final temperature of the mixture.

To find the final temperature of the mixture, we can use the principle of conservation of energy. The heat lost by the hotter water is equal to the heat gained by the colder water.

First, we need to calculate the heat lost by the hotter water. This can be done using the formula:

Q = m × c × ΔT

Where:
Q is the heat lost/gained
m is the mass of the substance
c is the specific heat capacity
ΔT is the change in temperature

For the hotter water:
m = 65.0 g
c = 4.184 J/g×K
ΔT = final temperature - initial temperature = final temperature - 87.5 °C

Next, we need to calculate the heat gained by the colder water. This can be done using the same formula:

For the colder water:
m = 35.0 g
c = 4.184 J/g×K
ΔT = final temperature - initial temperature = final temperature - 22.7 °C

Since the heat lost by the hotter water is equal to the heat gained by the colder water, we can set up the following equation:

m₁ × c × (final temperature - 87.5 °C) = m₂ × c × (final temperature - 22.7 °C)

Substituting the given values, we can solve for the final temperature.

65.0 g × 4.184 J/g×K × (final temperature - 87.5 °C) = 35.0 g × 4.184 J/g×K × (final temperature - 22.7 °C)

Now, we can solve the equation to find the numerical value of the final temperature.