If you pour 40g of refrigerated milk (at 4 degrees C) into 200g of freshly percolated coffee (at 96 degrees C), what would the final temperature of your coffee be?

Milk has a specific heat capacity of s=3.93J/g degrees C.
Coffee has a specific heat capacity of s=4.18J/g degrees C.
Assume that no heat is lost to the mug or to the surroundings.

Hint.heat lost by coffee=heat gained by milk

To find the final temperature of the coffee after mixing it with milk, you can use the principle of heat exchange.

First, calculate the heat lost by the coffee. This can be done using the formula:

Q = m * s * ΔT,

where:
Q is the heat lost (or gained),
m is the mass of the object,
s is the specific heat capacity of the substance,
ΔT is the change in temperature.

In this case, the mass of the coffee (m_coffee) is 200g, and the specific heat capacity (s_coffee) is 4.18J/g°C. The coffee was initially at 96°C, and we need to find the final temperature (T_final).

Heat lost by coffee = m_coffee * s_coffee * (T_initial - T_final)

Next, calculate the heat gained by the milk. The mass of the milk (m_milk) is 40g, and the specific heat capacity (s_milk) is 3.93J/g°C. The milk was initially at 4°C.

Heat gained by milk = m_milk * s_milk * (T_final - T_initial)

According to the hint given, the heat lost by the coffee is equal to the heat gained by the milk. So, we can set up an equation:

m_coffee * s_coffee * (T_initial - T_final) = m_milk * s_milk * (T_final - T_initial)

Now, we can substitute the known values:

200g * 4.18J/g°C * (96°C - T_final) = 40g * 3.93J/g°C * (T_final - 4°C)

Simplify the equation:

836.8g°C * (96°C - T_final) = 157.2g°C * (T_final - 4°C)

Expand the equation:

80268.8g°C - 836.8g°C * T_final = 157.2g°C * T_final - 628.8g°C

Combine like terms:

995.6g°C * T_final = 79640g°C

Divide both sides by 995.6g°C:

T_final = 80°C

Therefore, the final temperature of the coffee after mixing it with refrigerated milk would be 80°C.