What would be the final temperature of a mixture of 50 g of 15 degrees C water and 50 g of 40 degrees C water?

To find the final temperature of the mixture, you can use the principle of conservation of energy, specifically the law of heat exchange, known as the equation for heat transfer:

Q = m * c * ΔT

Where:
Q is the heat transferred (in joules),
m is the mass of the substance (in grams),
c is the specific heat capacity (in joules per gram-degree Celsius), and
ΔT is the change in temperature (final temperature - initial temperature) (in degrees Celsius).

To solve this problem, you need to calculate the heat transferred from the 40 degrees C water to the mixture and from the 15 degrees C water to the mixture, and then calculate the final temperature of the mixture.

Step 1: Calculate the heat transferred from the 40 degrees C water to the mixture:
Q_1 = m_water_1 * c_water * ΔT_water_1

Where:
m_water_1 = mass of the 40 degrees C water = 50 g
c_water = specific heat capacity of water = 4.18 J/g°C (approximate value)
ΔT_water_1 = change in temperature of the 40 degrees C water = final temperature - initial temperature = T_final - 40°C

Step 2: Calculate the heat transferred from the 15 degrees C water to the mixture:
Q_2 = m_water_2 * c_water * ΔT_water_2

Where:
m_water_2 = mass of the 15 degrees C water = 50 g
c_water = specific heat capacity of water = 4.18 J/g°C (approximate value)
ΔT_water_2 = change in temperature of the 15 degrees C water = final temperature - initial temperature = T_final - 15°C

Step 3: Set up the equation for heat conservation:
Q_1 + Q_2 = 0

Since the heat transferred from one water to the mixture is equal to the heat transferred from the other water to the mixture (since heat is conserved and no heat is lost to the surroundings).

Step 4: Solve for the final temperature (T_final):
Q_1 + Q_2 = 0
(m_water_1 * c_water * ΔT_water_1) + (m_water_2 * c_water * ΔT_water_2) = 0
(50 g * 4.18 J/g°C * (T_final - 40°C)) + (50 g * 4.18 J/g°C * (T_final - 15°C)) = 0

Solve the above equation to find the value of T_final, which will be the final temperature of the mixture of water.

Note: Calculations have been simplified by using the specific heat capacity of water as a constant, but it should be noted that the specific heat capacity of water is temperature-dependent and can vary slightly with different temperatures.