Suppose you mix 75 g of water at 15 °C with 25 g of water at 75 °C. Predict the final temperature

The 75 g of cold water must heat up 1/3 times as much as the 25 g of hot water cools down.

Of the initial 60 C temperature difference, the cold water heats up 1/4 of the 60 C, or 15 C.

The 75 g therefore heats to 15 + 15 = 30 C, while the 25g of hot water cools to 75 - 45 = 30 C

30 C is the answer

To predict the final temperature when two substances at different temperatures are mixed together, you need to use the principle of conservation of energy. The heat gained or lost by one substance is equal to the heat lost or gained by the other substance.

In this case, we have two quantities of water with different temperatures: 75 g at 15 °C and 25 g at 75 °C. To find the final temperature, we can use the following equation:

(mass1 * specific heat1 * change in temperature1) + (mass2 * specific heat2 * change in temperature2) = 0

Where:
- mass1 is the mass of the first substance (75 g)
- mass2 is the mass of the second substance (25 g)
- specific heat1 is the specific heat capacity of water (4.18 J/g°C)
- specific heat2 is also the specific heat capacity of water (4.18 J/g°C)
- change in temperature1 is the final temperature - initial temperature of the first substance (final temperature is unknown, initial temperature is 15 °C)
- change in temperature2 is the final temperature - initial temperature of the second substance (final temperature is unknown, initial temperature is 75 °C)

Now let's substitute these values into the equation and solve for the final temperature.

(75 g * 4.18 J/g°C * (final temperature - 15 °C)) + (25 g * 4.18 J/g°C * (final temperature - 75 °C)) = 0

(313.5 J/°C * final temperature - 4702.5 J) + (104.5 J/°C * final temperature - 2612.5 J) = 0

(313.5 J/°C * final temperature + 104.5 J/°C * final temperature) - (4702.5 J + 2612.5 J) = 0

418 J/°C * final temperature - 7315 J = 0

418 J/°C * final temperature = 7315 J

final temperature = 7315 J / 418 J/°C

final temperature ≈ 17.50 °C

Therefore, the predicted final temperature when 75 g of water at 15 °C is mixed with 25 g of water at 75 °C is approximately 17.50 °C.