Accurate Expressions for the Dewpoint and Frost Point Derived from the Rankine–Kirchhoff Approximations

Romps, David M.

doi:10.1175/jas-d-20-0301.1

Cited by 4 publications

(8 citation statements)

References 17 publications

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“…where T R is a reference temperature, and c f and c p,v are the constant pressure-specific heats of the fluid and vapor. See for example (Emanuel, 1994, p. 115), (Ambaum, 2020), or (Romps, 2021). In this section, we derive a sometimes-used alternative to Equation (2).…”

Section: An Accurate Expression For the Heat Of Vaporizationmentioning

confidence: 99%

“…which is separable and readily integrable. Integrating from the reference temperature, T R , to a temperature T gives the standard textbook relation Equation (13a) (Emanuel, 1994, p. 116), (Romps, 2021) ln…”

Section: Approximate Form Neglecting Fluid Volumementioning

confidence: 99%

“…The above equations for vapor pressure can be used to determine the relation between relative humidity and dew point temperature (Romps, 2021). The usual procedure is to define the atmosphere's relative humidity, H, as…”

Section: Impact Of the New Vapor Pressure Formula On The Relation Of ...mentioning

confidence: 99%

“…The expression usually encountered for this is has a linear dependence in temperature,

T

h_{italicfg} (T) \equiv h_{v} (T) - h_{f} (T) = h_{italicfg} (T_{R}) - (c_{f} - c_{p, v}) (T - T_{R})

where

T_{R}

is a reference temperature, and

c_{f}

and

c_{p, v}

are the constant pressure‐specific heats of the fluid and vapor. See for example (Emanuel, 1994, p. 115), (Ambaum, 2020), or (Romps, 2021). In this section, we derive a sometimes‐used alternative to Equation ).…”

Section: An Accurate Expression For the Heat Of Vaporizationmentioning

confidence: 99%

“…After neglecting the terms in

v_{f}

, Equation ) becomes

\frac{1}{p_{italicsat} (T)} \frac{d p_{italicsat} (T)}{italicdT} = \frac{L^{0} - (c_{f} - c_{p, v}) T}{R_{v} T^{2}}

which is separable and readily integrable. Integrating from the reference temperature,

T_{R}

, to a temperature

T

gives the standard textbook relation Equation ) (Emanuel, 1994, p. 116), (Romps, 2021)

\ln (\frac{p_{sat} ((), T)}{p_{sat} ((), T_{R})}) = \frac{- L^{0}}{R_{v}} (\frac{1}{T} - \frac{1}{T_{R}}) - \frac{((), c_{f} goodbreak- c_{p, v})}{R_{v}} \ln (\frac{T}{T_{R}})

p_{italicsat} (T) = p_{italicsat} (T_{R}) {((), \frac{T}{T_{R}})}^{- (c_{f} - c_{p, v}) / R_{v}} \exp \{- \frac{L^{0}}{R_{v}} (\frac{1}{T} - \frac{1}{T_{R}})\}

Noting that

L^{0} = h_{italicfg} + <...

…”

Section: Integrating the Clapeyron Equationmentioning

confidence: 99%

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A note on integrating the Clapeyron equation without neglecting the specific fluid volume

Swanson¹

2023

Atmospheric Science Letters

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Under certain approximations, the Clapeyron equation can be integrated to yield a simple exponential relation giving the saturation vapor pressure over a condensed phase as a function of temperature. The derivation usually assumes that the vapor behaves as an ideal gas with constant specific heat, and that the fluid also has constant specific heat. In addition, the specific fluid volume is neglected in comparison with the specific vapor volume. In this case, the Clapeyron equation is separable and readily integrable in closed form. It is shown here that this latter assumption is not required. A simple closed‐form relation between saturation vapor pressure and temperature is derived which includes the condensed phase‐specific volume. Two examples of the use of this result are presented.

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Section: An Accurate Expression For the Heat Of Vaporizationmentioning

confidence: 99%

Section: Approximate Form Neglecting Fluid Volumementioning

confidence: 99%

Section: Impact Of the New Vapor Pressure Formula On The Relation Of ...mentioning

confidence: 99%

“…The expression usually encountered for this is has a linear dependence in temperature,

T

h_{italicfg} (T) \equiv h_{v} (T) - h_{f} (T) = h_{italicfg} (T_{R}) - (c_{f} - c_{p, v}) (T - T_{R})

where

T_{R}

is a reference temperature, and

c_{f}

and

c_{p, v}

Section: An Accurate Expression For the Heat Of Vaporizationmentioning

confidence: 99%

“…After neglecting the terms in

v_{f}

, Equation ) becomes

\frac{1}{p_{italicsat} (T)} \frac{d p_{italicsat} (T)}{italicdT} = \frac{L^{0} - (c_{f} - c_{p, v}) T}{R_{v} T^{2}}

which is separable and readily integrable. Integrating from the reference temperature,

T_{R}

, to a temperature

T

gives the standard textbook relation Equation ) (Emanuel, 1994, p. 116), (Romps, 2021)

\ln (\frac{p_{sat} ((), T)}{p_{sat} ((), T_{R})}) = \frac{- L^{0}}{R_{v}} (\frac{1}{T} - \frac{1}{T_{R}}) - \frac{((), c_{f} goodbreak- c_{p, v})}{R_{v}} \ln (\frac{T}{T_{R}})

p_{italicsat} (T) = p_{italicsat} (T_{R}) {((), \frac{T}{T_{R}})}^{- (c_{f} - c_{p, v}) / R_{v}} \exp \{- \frac{L^{0}}{R_{v}} (\frac{1}{T} - \frac{1}{T_{R}})\}

Noting that

L^{0} = h_{italicfg} + <...

…”

Section: Integrating the Clapeyron Equationmentioning

confidence: 99%

See 3 more Smart Citations

A note on integrating the Clapeyron equation without neglecting the specific fluid volume

Swanson¹

2023

Atmospheric Science Letters

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On Moist Potential Temperatures and Their Ability to Characterize Differences in the Properties of Air Parcels

Marquet

Stevens

2022

Journal of the Atmospheric Sciences

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A framework is introduced to compare moist “potential” temperatures. The equivalent potential temperature θe, the liquid water potential temperature θℓ, and the entropy potential temperature θs are all shown to be potential temperatures, in the sense that they measure the temperatures of certain reference-state systems whose entropy is the same as that of the air parcel. They only differ in the choice of reference-state composition—θℓ describes the temperature a condensate-free state, θe a vapor-free state, and θs a water-free state—required to have the same entropy as the given state. Although in this sense θe, θℓ, and θs are all different flavors of the same thing, only θℓ satisfies the stricter definition of a “potential temperature,” as corresponding to a reference temperature accessible by an isentropic and closed transformation of a system in equilibrium; both θe and θℓ measure the “relative” enthalpy of an air parcel at their respective reference states, but only θs measures air-parcel entropy. None mix linearly, but all do so approximately, and all reduce to the dry potential temperature θ in the limit as the water mass fraction goes to zero. As is well known, θ does mix linearly and inherits all the favorable (entropic, enthalpic, and potential temperature) properties of its various—but descriptively less rich—moist counterparts. All involve quite complex expressions, but admit relatively simple and useful approximations. Of the three moist “potential” temperatures, θs is the least familiar, but the most well mixed in the broader tropics, a property that merits further study as a possible basis for constraining mixing processes.

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Polar Stratospheric Clouds Observations at Concordia Station by the Remotely Controlled Lidar Observatory

Di Liberto,

Colao,

Serva

et al. 2024

Preprint

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Polar stratospheric clouds (PSCs) form in polar regions typically between 15 and 25 km, when the local temperature is sufficiently low. PSCs play an important role in the ozone chemistry and the dehydration and denitrification of the stratosphere. Lidars with a depolarization channel may be used to detect and classify different classes of PSCs. The main PSC classes are water ice, nitric acid trihydrate (NAT) and supercooled ternary solutions (STS), the latter being liquid droplets consisting of water, nitric acid and sulphuric acid. PSCs have been observed at the lidar observatory at Concordia Station from 2014 on. The harsh environmental conditions at Concordia during winter render successful lidar operation difficult. In order to facilitate the operation of the observatory several measures have been put in place to achieve an almost complete remote control of the system. PSC occurrence is strongly correlated with local temperatures and is affected by dynamics, as the PSC coverage during the observation season shows.

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Accurate Expressions for the Dewpoint and Frost Point Derived from the Rankine–Kirchhoff Approximations

Cited by 4 publications

References 17 publications

A note on integrating the Clapeyron equation without neglecting the specific fluid volume

A note on integrating the Clapeyron equation without neglecting the specific fluid volume

On Moist Potential Temperatures and Their Ability to Characterize Differences in the Properties of Air Parcels

Polar Stratospheric Clouds Observations at Concordia Station by the Remotely Controlled Lidar Observatory

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