What would be the final temperature of a mixture of 50 g of 20 0C water and 50 g of 40 0C water. I'm really not sure how to do this do I need to convert 20 Celsius to Fahrenheit to start? what are the steps for this?
Ah, the temperature mixture problem! Don't worry, I'll clown around and help you out!
To answer your question, you don't actually need to convert temperatures from Celsius to Fahrenheit. The good news is, we can work with Celsius directly.
Now, let's find the final temperature of the mixture. We can use the principle of conservation of energy, which states that the total heat gained by the cooler water should be equal to the total heat lost by the hotter water.
Here's what we can do:
Step 1: Calculate the heat gained by the cooler water. We'll use the formula: Q = m * C * ΔT, where Q represents the heat gained, m is the mass, C is the specific heat capacity, and ΔT is the change in temperature.
For the 20°C water, the heat gained can be calculated as:
Q1 = 50g * 4.18 J/g°C * (final temperature - 20°C)
Step 2: Calculate the heat lost by the hotter water. Using the same formula, we have:
Q2 = 50g * 4.18 J/g°C * (40°C - final temperature)
Step 3: Since heat gained equals heat lost, we can set up an equation:
Q1 = Q2
Now, let's solve that equation for the final temperature!
50g * 4.18 J/g°C * (final temperature - 20°C) = 50g * 4.18 J/g°C * (40°C - final temperature)
Simplifying, we get:
4.18 * (final temperature - 20) = 4.18 * (40 - final temperature)
Now, solve for the final temperature, and remember to keep your laughter handy in case you get stuck along the way!
To find the final temperature of the mixture, you don't need to convert Celsius to Fahrenheit. You can use the principle of conservation of energy, which states that the total heat gained by one part of a system is equal to the total heat lost by another part of the system.
To calculate the final temperature, follow these steps:
1. Determine the heat gained by the colder water mass:
Heat gained = mass of cold water × specific heat capacity of water × temperature change
In this case:
Mass = 50 g
Specific heat capacity of water = 4.18 J/g°C (joules per gram Celsius)
Temperature change = final temperature - initial temperature = Tf - 20°C
2. Determine the heat lost by the hotter water mass:
Heat lost = mass of hot water × specific heat capacity of water × temperature change
In this case:
Mass = 50 g
Specific heat capacity of water = 4.18 J/g°C
Temperature change = final temperature - initial temperature = 40°C - Tf
3. Equate the heat gained and heat lost:
Heat gained = Heat lost
(50 g) × (4.18 J/g°C) × (Tf - 20°C) = (50 g) × (4.18 J/g°C) × (40°C - Tf)
4. Solve the equation for Tf (final temperature) using algebra:
Multiply out both sides of the equation and simplify to get:
4.18 × 50 × Tf - 83.6 = 4.18 × 50 × 40 - 4.18 × 50 × Tf
Combine like terms:
4.18 × 50 × Tf + 4.18 × 50 × Tf = 4.18 × 50 × 40 + 83.6
Simplify further:
8.36 × 50 × Tf = 8.36 × 50 × 40 + 83.6
Divide both sides by 8.36 × 50:
Tf = (8.36 × 50 × 40 + 83.6) / (8.36 × 50)
Simplify and calculate:
Tf = (16680 + 83.6) / 418
Tf = 16763.6 / 418
Tf ≈ 40.12°C
Therefore, the final temperature of the mixture is approximately 40.12°C.
To find the final temperature of a mixture of water at different initial temperatures, you don't need to convert Celsius to Fahrenheit, as the Celsius scale is sufficient for calculations. You can use the principle of energy conservation, which states that the total energy of the system remains constant.
Here are the steps to solve the problem:
1. Determine the masses and initial temperatures of the two water samples. In this case, you have 50 g of water at 20 °C and 50 g of water at 40 °C.
2. Calculate the heat gained or lost by each water sample using the formula: Q = m * c * ΔT, where Q is the heat energy gained or lost, m is the mass, c is the specific heat capacity of water (which is 4.18 J/g°C), and ΔT is the change in temperature.
For the 20 °C water:
Q1 = 50 g * 4.18 J/g°C * (final temperature - 20 °C)
For the 40 °C water:
Q2 = 50 g * 4.18 J/g°C * (final temperature - 40 °C)
3. Apply the principle of energy conservation: Since the total energy remains constant, the heat gained by one water sample should be equal to the heat lost by the other sample. Therefore, Q1 + Q2 = 0.
Substituting the expressions for Q1 and Q2:
50 g * 4.18 J/g°C * (final temperature - 20 °C) + 50 g * 4.18 J/g°C * (final temperature - 40 °C) = 0
4. Simplify the equation and solve for the final temperature.
50 * 4.18 * (final temperature - 20) + 50 * 4.18 * (final temperature - 40) = 0
2.09 * (final temperature - 20) + 2.09 * (final temperature - 40) = 0
2.09 * final temperature - 41.8 + 83.6 = 0
2.09 * final temperature = 41.8
final temperature = 41.8 / 2.09
Therefore, the final temperature of the mixture is 20 °C.
Note: In this case, the masses of the two water samples are equal, so the final temperature is the average of the initial temperatures.