Question

An eccentric chemistry professor stops in for coffee every day and orders 200 mL at precisely 75°C. You need to add enough milk at 5°C to drop the temperature of the coffee initially at 85°C to the desired order temperature. What is the temperature of the milk that needs to be added?

Answer 1

To achieve the desired temperature of 75°C, the milk added to the 85°C coffee should be at approximately 55°C.

Step-by-step explanation:

To determine the temperature of the milk needed to achieve the desired 75°C, we can use the heat transfer equation:

Q=mcΔT

where

Q is the heat transferred, m is the mass, c is the specific heat, and

ΔT is the change in temperature.

The heat lost by the coffee should equal the heat gained by the milk to reach thermal equilibrium.

`m coffee​ c coffee​ (T initial coffee​ −T final​ )=m milk​ c milk​ (T final​ −T initial milk​ )`
`m coffee​ c coffee​ (T initial coffee​ −T final​ )=m milk​ c milk​ (T final​ −T initial milk )`

Given that

m coffee =200g, coffee=4.18 J/g°C c coffee =4.18J/g°C, initial coffee =85

T initial coffee=85°C, final=75°T final =75°C, milk =4.18J/g°C c milk =4.18J/g°C, and initial milk=5°T initial milk =5°C, we can rearrange the equation to solve for final

T final and find that T final ≈55°C.

Therefore, to achieve the desired temperature of 75°C, the milk should be added at around 55°C. This ensures that the heat lost by the hot coffee is equal to the heat gained by the cold milk, resulting in the desired final temperature.

Therefore, to achieve the desired temperature of 75°C, the milk should be added at around 55°C. This ensures that the heat lost by the hot coffee is equal to the heat gained by the cold milk, resulting in the desired final temperature.