The forum discussion centers on calculating energy and mass in an espresso machine context, specifically heating milk and analyzing coffee cooling. For heating 150 g of milk from 20 °C to 80 °C, the energy required is 36,000 J, and the mass of steam condensed is calculated to be 15.8 g. The cooling of coffee is analyzed, with the conclusion that the cooling rate is not exponential, and the estimated temperature after 12 minutes is 29 °C. Key calculations involve specific heat capacities of milk and water, as well as the latent heat of steam.
PREREQUISITESStudents in physics or engineering, thermodynamics enthusiasts, and anyone involved in culinary science or espresso machine technology will benefit from this discussion.
In that case it indeed can be described by exponential. I though the numbers should be exactly the same, and not somewhat similar like in my case.TSny said:In the video, the numbers were chosen to make the percent change exactly 50% for two consecutive data points. For real data, you cannot expect the data to be perfectly exponential, or perfectly linear, etc. You are just trying to discover if the data is "well described" by exponential behavior, or linear behavior, etc.
For the data in the problem, the percent decrease is fairly constant at around 15%. If you had to pick between exponential or linear behavior, which would you choose?
For determining the temperature at t = 12 s, I would not recommend your method.
First get the temperature at t = 10 seconds using an assumption of exponential behavior. Then go to t = 12 s.moenste said:Do you have a suggestion how to find the temperature at t = 12 s?
But what percentage to use?TSny said:First get the temperature at t = 10 seconds using an assumption of exponential behavior. Then go to t = 12 s.