<p>There is a convention for moist air entropy built from dry air entropy being 0 at T = 273.15K and P = 101325Pa, and liquid water entropy being 0 at its triple point. See the page numbered 47 of this NIST document:</p>

<p><a href="http://www.nist.gov/calibrations/upload/5241.pdf" rel="nofollow">http://www.nist.gov/calibrations/upload/5241.pdf</a></p>

<p>Entropy is not measured directly.  </p>

<p>Entropy $S$ is defined as $dS \equiv dQ_{rev}/T$</p>

<p>Therefore, entropy can measured by measuring heat transfer and temperature. </p>

<p>See <a href="http://web.mit.edu/16.unified/www/SPRING/propulsion/notes/node40.html" rel="nofollow">Calculation of Entropy Change in Some Basic Processes</a> for more information.</p>

CC BY-SA 3.0
2014-05-20T13:04:37.200Z
2014-05-21T10:07:18.710Z
2014-05-21T10:07:18.710Z
DavePhD
<p>It is possible to compute the relevant moist air entropy by using the Third law values. This has been done first by Hauf and Höller (1987). A moist-air potential temperature has been defined by Marquet (2011, ..., 2017). This  moist-air potential temperature is truly synonymous with the moist-air entropy and is different from the previous values published by Emanuel or Pauluis, because the Third law values generate a new term which has large physical impacts.</p>

<hr>

<p>Hauf, T., and H. Höller, 1987: Entropy and potential temperature.
J. Atmos. Sci., 44 (20), 2887–2901</p>

<p>Marquet, P., 2011: Definition of a moist entropy potential temperature:
application to FIRE-I data flights. Quart. J. Roy. Meteorol.
Soc., 137 (9), 768–791</p>

<p>Marquet, P., 2017: A third-law isentropic analysis of a simulated
hurricane. J. Atmos. Sci., 74 (10), 3451–3471</p>

CC BY-SA 4.0
2018-05-18T13:32:01.977Z
2018-05-18T13:32:01.977Z
Pascal Marquet
<p>Here's a paper on the <a href="http://www.math.nyu.edu/~pauluis/Olivier_Pauluis_Homepage/Bibliography_files/Pauluis_Held_2002a.pdf" rel="nofollow">entropy budget</a><sup>1</sup>, where moist entropy is defined in equation (8) as</p>

<blockquote>
  <p>$$
s = (1-q_t)(C_{pd} \ln T - R_d \ln p_d) + q_t C_l \ln T + \frac{q_v L_v}{T} - q_v R_v \ln \mathcal{H} 
$$</p>
  
  <p>In this expression, $q_v$ is the speciﬁc humidity for water vapor, $C_{pd}$ is the speciﬁc heat at constant pressure of dry air, $C_l$ is the speciﬁc heat of liquid water, $T$ is the temperature of moist air, $R_d$ and $R_v$ are the gas constants of dry air and water vapor, $p_d$ is the partial pressure of dry air, $\mathcal{H} = e/e_s$ is the relative humidity, $e$ is the water vapor pressure, and $e_s$ is the saturation vapor pressure.</p>
</blockquote>

<p>I'm just curious: is entropy directly measured, or indirectly measured from other sources? If we measured it, what would be the spatial-temporal resolution of such a measurement?</p>

<hr>

<p><sup>1</sup> Pauluis, Olivier, and Isaac M. Held. "Entropy Budget of an Atmosphere in Radiative–Convective Equilibrium. Part I: Maximum Work and Frictional Dissipation." <em>Journal of the Atmospheric Sciences</em> 59: 125-139. </p>

CC BY-SA 3.0
2014-04-15T22:07:48.237Z
Is the answer not in the paper or its references?
gerrit
CC BY-SA 3.0
2014-04-15T22:11:27.277Z
It's a very theoretical paper, so it doesn't discuss measurement much. It's also back from 1991, so I suspect that there are more ways to measure it now. But it still doesn't seem to be a very well-researched topic.
InquilineKea
CC BY-SA 3.0
2014-04-15T22:12:19.860Z
I don't know, but I strongly expect it's *not* directly measured.
gerrit
CC BY-SA 3.0
2014-04-16T11:19:51.207Z
I don't really understand why that paper is linked from the question. Is there anything it says that adds to the question? If so, could you perhaps quote that bit, instead of just linking to the whole paper?
naught101
<meteorology><atmosphere><thermodynamics>
How do we measure (or empirically calculate) the amount of entropy in the atmosphere and oceans?
InquilineKea
# How do we measure (or empirically calculate) the amount of entropy in the atmosphere and oceans?

(Asked by: username_0 on 2014-04-15)

Here's a paper on the [entropy budget](http://www.math.nyu.edu/~pauluis/Olivier_Pauluis_Homepage/Bibliography_files/Pauluis_Held_2002a.pdf)1, where moist entropy is defined in equation (8) as

> $$
> s = (1-q\_t)(C\_{pd} \ln T - R\_d \ln p\_d) + q\_t C\_l \ln T + \frac{q\_v L\_v}{T} - q\_v R\_v \ln \mathcal{H}
> $$
>
> In this expression, $q\_v$ is the speciﬁc humidity for water vapor, $C\_{pd}$ is the speciﬁc heat at constant pressure of dry air, $C\_l$ is the speciﬁc heat of liquid water, $T$ is the temperature of moist air, $R\_d$ and $R\_v$ are the gas constants of dry air and water vapor, $p\_d$ is the partial pressure of dry air, $\mathcal{H} = e/e\_s$ is the relative humidity, $e$ is the water vapor pressure, and $e\_s$ is the saturation vapor pressure.

I'm just curious: is entropy directly measured, or indirectly measured from other sources? If we measured it, what would be the spatial-temporal resolution of such a measurement?

---

1 Pauluis, Olivier, and Isaac M. Held. "Entropy Budget of an Atmosphere in Radiative–Convective Equilibrium. Part I: Maximum Work and Frictional Dissipation." *Journal of the Atmospheric Sciences* 59: 125-139.

**Tags:** meteorology, atmosphere, thermodynamics

> **Comments:**
> **username_1**: Is the answer not in the paper or its references?  
> **username_0**: It's a very theoretical paper, so it doesn't discuss measurement much. It's also back from 1991, so I suspect that there are more ways to measure it now. But it still doesn't seem to be a very well-researched topic.  
> **username_1**: I don't know, but I strongly expect it's *not* directly measured.  
> **username_2**: I don't really understand why that paper is linked from the question. Is there anything it says that adds to the question? If so, could you perhaps quote that bit, instead of just linking to the whole paper?  

---

## 2 answers

### Answer by username_3 on 2014-05-20. Score: 6

There is a convention for moist air entropy built from dry air entropy being 0 at T = 273.15K and P = 101325Pa, and liquid water entropy being 0 at its triple point. See the page numbered 47 of this NIST document:

<http://www.nist.gov/calibrations/upload/5241.pdf>

Entropy is not measured directly.

Entropy $S$ is defined as $dS \equiv dQ\_{rev}/T$

Therefore, entropy can measured by measuring heat transfer and temperature.

See [Calculation of Entropy Change in Some Basic Processes](http://web.mit.edu/16.unified/www/SPRING/propulsion/notes/node40.html) for more information.


---

### Answer by username_4 on 2018-05-18. Score: 2

It is possible to compute the relevant moist air entropy by using the Third law values. This has been done first by Hauf and Höller (1987). A moist-air potential temperature has been defined by username_4 (2011, ..., 2017). This moist-air potential temperature is truly synonymous with the moist-air entropy and is different from the previous values published by Emanuel or Pauluis, because the Third law values generate a new term which has large physical impacts.

---

Hauf, T., and H. Höller, 1987: Entropy and potential temperature.
J. Atmos. Sci., 44 (20), 2887–2901

username_4, P., 2011: Definition of a moist entropy potential temperature:
application to FIRE-I data flights. Quart. J. Roy. Meteorol.
Soc., 137 (9), 768–791

username_4, P., 2017: A third-law isentropic analysis of a simulated
hurricane. J. Atmos. Sci., 74 (10), 3451–3471


---

