Thermodynamics yes or no Q (with explanation)

[Fancy Moses]

Homework Statement

Would it be possible for a changing ambient air temperature profile (e.g. 30ºC for X hours immediately changing to 35ºC for Y hours immediately changing to 25ºC for Z hours) to effect a certain mass and result in a temperature change EQUAL to a separate, constant ambient air temperature effecting a similar mass?

Homework Equations

Not sure...

Other than total time of profile 2 = X+Y+Z hours (from profile 1)

The Attempt at a Solution

I thought I could integrate the initial temperature profile, find the area under the curve, and create a similar area with a constant temperature rectangle with temperature = height on Y axis and time of the profile being length on the x-axis which would be equal to the total time of the original ambient air profile. I'm not sure if this corresponds directly to temperature change of the mass, but logically it makes sense.

I might be able to clarify more, but that's the question which was posed.

 

[KataKoniK]

I appreciate your curiosity and attempt at a solution. The short answer to your question is yes, it is possible for a changing ambient air temperature profile to result in a similar temperature change in a certain mass as a constant ambient air temperature. However, the specific conditions and variables involved would determine the extent of this similarity.

In order to accurately determine the temperature change in a certain mass, we would need to consider factors such as the specific heat capacity of the mass, the rate of heat transfer between the mass and the surrounding air, and the duration and magnitude of the temperature changes in the ambient air.

Integrating the initial temperature profile and creating a similar area with a constant temperature rectangle may give you a rough estimate, but it may not account for all the variables involved. Additionally, it is important to keep in mind that temperature changes in a mass are not always linear and can be affected by external factors such as wind and humidity.

To accurately determine the temperature change in a certain mass in response to a changing ambient air temperature profile, it would be best to conduct experiments or use mathematical models that take into account all the relevant variables. I hope this helps and encourages further exploration into this topic.

 

[Mene]

I would say that the answer to this question is "yes." Thermodynamics is the study of energy and its transformation, and in this scenario, we are dealing with the transfer of thermal energy from the ambient air to a certain mass. According to the First Law of Thermodynamics, energy cannot be created or destroyed, only transferred from one form to another. Therefore, the changing ambient air temperature profile would still result in a temperature change in the mass, just as a constant ambient air temperature would.

The attempt at a solution that the student has proposed seems logical and could potentially provide a way to compare the two scenarios. However, it is important to note that there are likely other factors at play that could affect the temperature change in the mass, such as the specific heat capacity of the material, the rate of heat transfer, and any internal energy sources within the mass. These factors would need to be taken into consideration in order to accurately compare the two scenarios.

In conclusion, thermodynamics does play a role in this scenario and the changing ambient air temperature profile would indeed have an effect on the temperature of the mass. However, further analysis and consideration of other factors would be needed to fully understand and compare the two scenarios.