I'm working on a problem related to entropy, and for this particular use case it's advantageous to write down properties in 'specific' units. In the case of entropy (with units Joules over Kelvin, I think is commonly referred to as: $[S] = \pu{J K-1}$), I want to know how to communicate volumetric entropy, i.e. Joules per cubic meter Kelvin: $[\color{red}{?}] = \pu{J K-1 m-3 }$.

Is it something like $\bar{S}$?

  • $\begingroup$ Are you looking for an analogue to specific volume or the specific gas constant? $\endgroup$ – Todd Minehardt Nov 25 '17 at 23:58
  • $\begingroup$ No I'm wondering if the notation is different for the intrinsic property of entropy. Specific entropy is useful in fields such as chemistry and thermodynamics to compare substances. Here's a link to a thermodynamic table using specific entropy (in that case, kg in the denominator) $\endgroup$ – cbcoutinho Nov 26 '17 at 0:57
  • $\begingroup$ I'd definitely go with the IUPAC answer as a default, but just so you know, a lot of times people will use a \hat character over the (capital) symbol to denote "specific". That's pretty common in introductory thermodynamics textbooks. Koretsky's text comes to mind. $\endgroup$ – Argon Nov 26 '17 at 6:02

Specific entropy

According to IUPAC "Green Book" Quantities, units, and symbols in physical chemistry, specific entropy is denoted as lowercase latin "s": $s$ [1, p. 56], whereas $\bar{S}$ would refer to molar entropy:

\begin{array}{lll} \text{Name} & \text{Symbol} & \text{Definition} & \text{SI unit} & \text{Notes} \\ \hline [...]\\ \text{molar quantity}~X & X_\mathrm{m}, (\bar{X}) & X_\mathrm{m} = X/n & [X]/\pu{mol} & 5,6 \\ \text{specific quantity}~X & x & x = X/m & [X]/\pu{kg} & 5,6 \\ [...]\\ \end{array} [...]

$(5)$ The definition applies to pure substance. However, the concept of molar and specific quantities (see Section 1.4. p. 6) may also be applied to mixtures, n is the amount of substance (see Section 2.10, notes 1 and 2, p. 47).

$(6)$ $X$ is an extensive quantity, whose SI unit is $[X]$. In the case of molar quantities the entities should be specified.

Example $V_\mathrm{m,\ce{B}} = V_\mathrm{m}(\ce{B}) = V/n$ denotes the molar volume of $\ce{В}$.

Just as specific heat capacity $c$, specific entropy $s$ is measured in $\pu{J K-1 kg-1}$ [1, p. 90].

General note [1, p. 6]:

The adjective specific before the name of an extensive quantity is used to mean divided by mass. When the symbol for the extensive quantity is a capital letter, the symbol used for the specific quantity is often the corresponding lower case letter.

Volumetric entropy

Quite often there is no special notation used, and volumetric entropy is denoted with $S$. Specifically, volumetric entropy generation rate for the convective heat transfer in flowing viscous fluid is often denoted with S-prime notation, e.g. from classical paper "A Study of Entropy Generation in Fundamental Convective Heat Transfer" [2]:

\begin{align} & S' & [\pu{W K-1 m-1}] \\ & S'' & [\pu{W K-1 m-2}] \\ & S''' & [\pu{W K-1 m-3}] \end{align}


  1. IUPAC “Green Book”. Quantities, units, and symbols in physical chemistry, 3rd ed.; Cohen, R. E., Mills, I., Eds.; IUPAC Recommendations; RSC Pub: Cambridge, UK, 2007. ISBN 978-0-85404-433-7.
  2. Bejan, A. J. Heat Transfer 1979, 101 (4), 718–725. DOI: 10.1115/1.3451063.
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    $\begingroup$ Thank you, that's exactly the kind of information i was looking for. $\endgroup$ – cbcoutinho Nov 26 '17 at 4:32

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