How much milk at 10 degrees would need to be added to 250 ml of coffee at 95 degrees celsius to cool the coffee to 90 degrees celsius

[mass milk x specific heat milk x (Tfinal-Tinitial)] + [mass coffee x specific heat coffee x (Tfinal-Tinitial)] = 0

Tfinal = 90
Tinitial = 95
I assume specific heat milk and coffee to be the same as specific heat H2O.

To calculate the amount of milk at 10 degrees Celsius needed to cool the coffee from 95 degrees Celsius to 90 degrees Celsius, we can use the principle of heat transfer:

The heat lost by the coffee = the heat gained by the milk

First, let's calculate the heat lost by the coffee:

Heat lost by the coffee = mass of coffee × specific heat capacity of coffee × change in temperature

We know the volume of coffee is 250 ml, but we need to find its mass. Assuming the density of coffee is approximately the same as water, which is 1 g/ml, the mass will be 250 grams.

The specific heat capacity of coffee is similar to water, which is approximately 4.18 J/g°C.

Change in temperature = final temperature - initial temperature = 90°C - 95°C = -5°C (Note: Negative because the coffee is losing heat)

Heat lost by the coffee = 250 g × 4.18 J/g°C × -5°C = -5225 J (Joules)

Now, let's calculate the heat gained by the milk:

Heat gained by the milk = mass of milk × specific heat capacity of milk × change in temperature

Since we know the final temperature of the milk is 90°C, we can assume the mass of milk required to cool the coffee will be the same as the mass of coffee.

Change in temperature = final temperature - initial temperature = 90°C - 10°C = 80°C

The specific heat capacity of milk is approximately 4.18 J/g°C.

Heat gained by the milk = 250 g × 4.18 J/g°C × 80°C = 83600 J (Joules)

Now, we can set up the equation:

Heat gained by the milk = Heat lost by the coffee

83600 J = -5225 J

To equalize the heat, we need to add an equal amount of milk at 10 degrees Celsius, which is approximately 83600 J.

Therefore, you would need to add 250 ml (or grams) of milk at 10 degrees Celsius to cool the coffee to 90 degrees Celsius.

To find out how much milk at 10 degrees Celsius needs to be added to cool the coffee from 95 degrees Celsius to 90 degrees Celsius, we can use the principle of heat transfer.

The heat gained or lost by a substance can be calculated using the formula Q = mcΔT, where Q is the heat transferred, m is the mass of the substance, c is the specific heat capacity, and ΔT is the change in temperature.

In this case, the heat lost by the coffee will be equal to the heat gained by the milk. We want the final temperature of the coffee to be 90 degrees Celsius, so the temperature change for the coffee is ΔT = (95 - 90) = 5 degrees Celsius.

Now, let's assume the specific heat capacity of coffee and milk are equal. To make it easier, let's also assume the specific heat capacity (c) is equal to 1 (although in reality, it may differ slightly).

The heat gained by the milk can be calculated as Q_milk = mcΔT_milk, where ΔT_milk = (90 - 10) = 80 degrees Celsius, since we want the milk to warm up from 10 degrees Celsius to 90 degrees Celsius.

To find the mass of the milk required, we can set up the equation as follows:

Q_milk = Q_coffee

m_milk * c * ΔT_milk = m_coffee * c * ΔT_coffee

m_milk * ΔT_milk = m_coffee * ΔT_coffee

m_milk = (m_coffee * ΔT_coffee) / ΔT_milk

Now, substituting the values,

m_milk = (250 * 5) / 80

m_milk ≈ 15.625 ml

Therefore, approximately 15.625 ml of milk at 10 degrees Celsius need to be added to 250 ml of coffee at 95 degrees Celsius to cool the coffee to 90 degrees Celsius.