Can TdS be computed using an area, time double integral of heat flux density?

In summary, TdS (change in entropy) can be computed using an area-time double integral of heat flux density, also known as the entropy production rate method. This method allows for a more accurate measurement of TdS by taking into account the spatial and temporal variations of heat flux density. However, it is only applicable in steady-state systems and assumes a constant heat flux density. The area-time double integral is calculated by integrating the heat flux density over the area and time of the system, typically using numerical methods. While there are alternative methods for computing TdS, the area-time double integral method is often preferred for its accuracy and ability to capture variations.
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kmarinas86
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Can the TdS by a system be calculated by taking the area, time double integral of the heat flux density?

If so, is it possible that this double-integral would take on an opposite sign if inside there was a dominating, growing black hole, where, I would presume, heat flows inwards, and not outwards? The divergence of the field inside the surface would therefore have an opposite sign, so would a growing blackhole therefore be a TdS reducer?
 
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Anyone?
 

Related to Can TdS be computed using an area, time double integral of heat flux density?

1. Can TdS be computed using an area, time double integral of heat flux density?

Yes, TdS (change in entropy) can be computed using an area-time double integral of heat flux density. This method is known as the entropy production rate method.

2. What is the significance of using an area-time double integral for computing TdS?

The use of an area-time double integral allows for a more accurate measurement of TdS, as it takes into account the spatial and temporal variations of heat flux density.

3. Are there any limitations to using this method for computing TdS?

Yes, this method is only applicable in steady-state systems where there is no change in temperature, pressure, or composition over time. It also assumes a constant heat flux density throughout the system.

4. How is the area-time double integral of heat flux density calculated?

The area-time double integral is calculated by integrating the heat flux density over the area and time of the system. This is typically done using numerical methods such as finite element analysis or finite difference method.

5. Are there any alternative methods for computing TdS?

Yes, there are other methods for computing TdS, such as the Clausius-Clapeyron equation or the Gibbs free energy change method. However, the area-time double integral method is often preferred due to its accuracy and ability to capture spatial and temporal variations.

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