Entropy change is defined as the amount of energy dispersed reversibly to or from the system at a specific temperature. Reversivility means that the temperature of the system must remain constant during the dispersal of energy to or from the system . But this criterion is only fulfilled during phase change &amp; isothermal processes. But not all processes maintain constant temperature;temperature may change constantly during the dispersal of energy to or from the system . To measure entropy change ,say, from 300 K &amp; 310 K, the range is divided into infinitesimal ranges ,then entropy is measured in that ranges and then is integrated . But I cannot understand how they have measured entropy change in that infinitesimal ranges as there will always be difference between the temperature however small the range might be . What is the intuition behind it? Change of entropy is measured at constant temperature,so how can it be measured in a range ? I know it is done by definite integration but can't getting the proper intuition . Also ,if by using definite integration to measure change, continuous graph must be there(like to measure change in velocity,area under the graph of acceleration is measured) . So what is the graph whose area gives change in entropy? Plz help me explaining these two questions.

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Entropy change is defined as the amount of energy dispersed reversibly to or from the system at a specific temperature. Reversivility means that the temperature of the system must remain constant during the dispersal of energy to or from the system . But this criterion is only fulfilled during phase change &amp;amp; isothermal processes. But not all processes maintain constant temperature;temperature may change constantly during the dispersal of energy to or from the system . To measure entropy change ,say, from   300  K &amp;amp;   310  K, the range is divided into infinitesimal ranges ,then entropy is measured in that ranges and then is integrated . But I cannot understand how they have measured entropy change in that infinitesimal ranges as there will always be difference between the temperature however small the range might be . What is the intuition behind it? Change of entropy is measured at constant temperature,so how can it be measured in a range ? I know it is done by definite integration but can&#039;t getting the proper intuition . Also ,if by using definite integration to measure change, continuous graph must be there(like to measure change in velocity,area under the graph of acceleration is measured) . So what is the graph whose area gives change in entropy? Plz help me explaining these two questions.

bamenyab4mxn · Accepted Answer

For a reversible addition of heat, the entropy change is   ∫            d      Q        T  , in other words the area under the graph of       1    T   against   Q (heat added to system).And yes, when a small amount of heat   Δ  Q is added, temperature T changes only a little, so             Δ      Q        T   is well-defined. When added up this gives the integral.

Yasmine Larson · Accepted Answer

Calorimetry is a nasty business. Whenever is possible entropy is measured by measuring mechanical parameters by taking advantage the Gibbs form of 2nd law. For example, if a thin rod is elastic then   d  U  =  T  d  S  +  σ  d  ϵ where   σ  ,  ϵ are the stress and strain. From the equality of derivatives you get             ∂      S              ∂      σ                  |        T    =  −            ∂      ϵ              ∂      T                  |        σ   the right side of which you can measure directly and then you can integrate with respect to stress at constant   T. Thus you only have to measure entropy as function of stress at one temperature, the rest you can get by measuring thermal expansion at constant stress.

Entropy change is defined as the amount of energy dispersed reversibly to or from the system at a sp

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