## PV = nRT

If P, V and n remain the same, T has to remain the same as well.

P and n are fixed in the troposphere, so the only degrees of freedom in the Ideal Gas Law equation are V and T.

During winter, V and T both decrease. Reduced sunlight causes the temperature and height of the troposphere to decrease. During summer, the temperature and height of the troposphere increase.

Just having fun
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### 39 Responses to PV = nRT

1. joletaxi says:

and also the surface of emission,

2. R. Shearer says:

Embedded in my mind, like that Farrah Fawcett poster.

3. Anthony S says:

There you have it, Steven just proved that unprecedented emissions of CO2 have irrevocably changed R, the gas constant, despite the fact that its supposed to be a constant. That’s just how evil man made CO2 is.

• I didn’t say anything about CO2

• Ben Vorlich says:

Steve,
The comment reads like British humour to me, it made me at Brit smile!

• nielszoo says:

The form Steven has shown is Ideal Gas Law for a perfect gas and Ru is the Universal Gas Constant, 8.314462 J/mol°K. It “automatically” adjusts for different gases as “n” is the number of moles of the gas.

Even if Steven had brought up CO2, the individual form of the gas law equation is PV=mRT where m is the mass of the gas and R is the individual gas constant which is R=Ru/M where M is the molecular weight of the gas mix. CO2’s value is 188.9 J/kg°K and is lower than N2, O2, Ar and CH4 so increasing it’s concentration (at the expense of one of those gases) lowers air’s R value from its current 286.9 J/kg°K which would make the equilibrium temperature lower. That’s one of the reasons the Climateers don’t like talking about Gas Law it kicks their CO2 boogyman out due to good old proven physics.

• mkelly says:

The same for specific heat, Cp. As CO2 is lower, about .844, air in general, 1.004, CO2 lowers the specific heat of the overall air.

4. Stephen Richards says:

That’s why this equation was invariably written as P ~ T.
It’s also partly why Venus is about 400°c and Mars about -40 °C.

and Earth ?

• nielszoo says:

Earth’s ideal equilibrium temperature, dry air without water vapor, is 289.25°K (16.1°C) at 1 bar.

• emsnews says:

But if Earth goes to TWO bars, the cops pick him up from the curb and put him in the drunk tank. 🙂

5. wayne says:

Can’t complain there. So far so good.

6. Jerry Gorline says:

Mars has about the same percentage of CO2 in the atmosphere, 95%, from out-gasing in the rocks. The difference is that the surface pressure on Mars is about 10 mb, and on Venus it’s more like 100 bars (atmospheres). The thickness of the atmosphere on Venus has a lot to do with the high surface temperature and proximity to the sun, slow rotation, etc. What is unique about the Earth is the oceans. Venus most likely had a significant amount of water vapor initially but the atmosphere never reached saturation so the H2O in the atmosphere eventually boiled off into space. Hansen noted this in his research (runaway greenhouse effect) but he made a critical error in the amount of influence the oceans had to keep the greenhouse effect in check. The empirical evidence continues to show that Hansen was wrong. If a theory does not match observations, it’s wrong (Richard Feynman).

I could drive Poisson’s equation from memory again but that would be showing off. It’s not difficult but still fun. Given: P = (rho)RT, dQ = (Cp)dT – (1/rho)dP, and dQ = 0. I’m predicting another colder than normal winter in the East. Keep up the good work Steven.

Best regards All,

JerryG

• emsnews says:

Mann went to too many bars before writing his papers. Thus, all the errors. 🙂 At least 100 bars, I bet.

• David Jay says:

After all, he was under a lot of pressure to “get rid of the MWP”

• Jerry Gorline says:

Pretty punny, considering that he tried so hard to argue that the MWP was just a local anomaly induced by a warm NAO, even though evidence keeps coming in that it was at least as warm as today, probably warmer, and global in scope (southern hemisphere signal). That’s Mann made global warming for ya, makes me wanna go to a bar or two and write dP/dz = -(rho)g on a napkin, and play with P = (rho)RT.

Hat tip to Mark Steyn, keep up the fight, for what is right. [1] Never give up, never surrender. [2]

JerryG

1. Beastie Boys (paraphrase).
2. Galaxy Quest, 1999.

7. KTM says:

It seems that runaway anthropogenic global warming (++T) would have to be accompanied by a measurable increase in atmospheric Pressure and/or Volume.

Have people attempted to track atmospheric pressures or volumes in a systematic way over the past several decades to corroborate the temperature changes they assert are happening?

Ideally the Pressure and/or Volume data would be collected as part of the same datasets used for temperature. Can they collect this data from satellites?

• Overall P stays the same because it equalizes at the surface (wind is caused by this).

It has to be V that changes.

• Ben says:

RE: — KTM — Have people attempted to track atmospheric pressures or volumes in a systematic way over the past several decades to corroborate the temperature changes they assert are happening?

KTM, They have.

http://www.nature.com/news/2003/030320/full/news030317-6.html

Here is a hilarious article from Nature 2003. The predictions they state have not come true. The “mild-not” winters in the US, the “reduced-rain-not” in Spain…

Just search google for spain flood and chuckle

8. Brian D says:

I found Trenberth’s missing heat. It showed up a few years ago. The warmer’s gas(hot air) law – make it look good.

• Brian D says:

Oh yeah, and make it look real good in 7 days. Can’t have all that blue stuff.

• Robert B says:

Don’t tell BOM. That is the sort of discontinuity that needs to homogenised by increasing the 2/27/2001 temperatures up.

9. “P and n are fixed in the troposphere, so the only degrees of freedom in the Ideal Gas Law equation are V and T.”

Well, in fact n is the only fixed constant in the ideal gas law. P is definitely not fixed, unless you make a false assumption that V and T are also fixed, or you are solely referring to the surface pressure, which as a global average of 1 atmosphere, but obviously the barometric pressure varies widely temporally and spatially.

Basically what you are claiming is that when the weather man is constantly talking about how high pressure systems and low pressure systems are the cause of weather patterns around the globe that this is all nonsense because P=constant in the troposphere and all of meteorology and the barometric formula tossed in the trash.

• “but obviously the barometric pressure varies widely temporally and spatially.”

No. Global P stays the same because it depends on the mass of the air. It may vary due to uneven heating (weather) but that is negligible, overall P stays the same.

Your third paragraph is weather.

• “but obviously the barometric pressure varies widely temporally and spatially.”

Morgan Wright says: No.

You didn’t understand the comment apparently – so here it is again with added bolding and additions so you’ll hopefully understand:

“Well, in fact n is the only fixed constant in the ideal gas law. P is definitely not fixed, unless you make a false assumption that V and T are also fixed, or you are solely referring to the surface pressure, which is by definition a global average of 1 atmosphere at all times at the latitude of Paris France, but obviously the barometric pressure at any one particular x, y, or z location varies widely temporally and spatially.”

And of course the global atmospheric pressure is constant by definition at 1 unit atmospheres at the latitude (and not other latitudes necessarily) of Paris, France BY definition.

Of course, “Global P stays the same because it depends on the mass of the air.” and by Newton’s second law of motion, F=ma, this becomes F=mg for the atmosphere to produce that gravitational pressure forcing at the surface, and hence the surface pressure (via the ideal gas law) + solar radiative forcing.

The barometric formula is in fact derived from this assumption F=mg for the atmosphere.

• So what? We are comparing Earth to Venus and you are worried about weather. The concept of average is very hard to grasp for some people.

• So Morgan Wright, since you’re the expert on all the planets, I’ve got a question for you about Uranus that I need your help on:

Please let me know what explains why there are storms at the top of the atmosphere on Uranus emitting to space more than 83,000 times the radiation Uranus receives from the Sun.

a) greenhouse gas backradiation
b) P
c) V
d) n
e) R
f) T

• KTM says:

Pressure is force over unit volume. If we assume that the mass of the atmosphere is constant (despite the GIGATONS of carbon being introduced that we keep hearing about), then the force of gravity on the atmosphere would also be constant.

However, if temperature is higher then the volume of the atmosphere would increase somewhat. Larger volume for a constant force = lower average pressure.

The actual numbers involved may be trivial in the big picture, but if they are claiming that atmospheric temperatures are changing by hundredths of a degree (trivial by any definition), then why wouldn’t we expect to see measurable changes in average pressure or volume of a similar magnitude?

• Volume has zero impact on atmospheric surface pressure.

10. Tony, can you explain why you have said many times surface T on Venus is due to pressure, but say the opposite for Earth?

• Venus has a higher n than Earth, by 90x.

P is determined by n and gravity. Gravity on Earth and Venus are the same so Venus has 90x more P than Earth.

PV = nRT

P and n on Venus are both 90 x Earth so cancel them out

V = RT but R is just a constant so:

V ~ T

Guess which planet has more V ~ T

• The mass of the Venus atmosphere is 4.8×10^20 kg, about 93 times the mass of the Earth’s total atmosphere, and the Pressure is thus ~93 bars compared to 1 bar on Earth [i.e. 93 times higher].

Of course the surface temperature is higher on Venus due to both 93 bars pressure and probable conduction downwards from the solar-heated opaque cloud tops, but so what, all that goes to show that pressure in every thick atmosphere increases surface temperature as I’m saying, so thanks for debunking yourself.

And please do explain how anything other than pressure on Uranus creates OLR from the TOP of the atmosphere outgoing to space that is 83,000X times greater than received from the Sun. Greenhouse gases, right?

• Chris Barron says:

“Of course the surface temperature is higher on Venus due to both 93 bars pressure and probable conduction downwards from the solar-heated opaque cloud tops, but so what, all that goes to show that pressure in every thick atmosphere increases surface temperature as I’m saying, so thanks for debunking yourself.”

This is true if you can contain the heat, and I don’t think you can because so much is lost to space. (or else every pressurised container would be hot if pressure increases temperature)

• “every pressurised container would be hot if pressure increases temperature”

Take the bicycle tire analogy. When you pressurize the tire it gets hotter for awhile, but then cools to ambient room temp by the tire convecting that heat.

Second situation is we have a leaky tire that we have to keep pumping to maintain the same pressure, so that tire remains hotter as long as compression of the air is a continuous process.

The atmosphere is only analogous to the second situation, since air packets are continuously warming at the surface then rise/expand/cool until equilibrium with surrounding air in upper atmosphere, then due to gravitational potential energy these air packets have accumulated then fall/compress/warm down to the surface.

This is how the troposphere temperature gradient from 220K-288K is entirely controlled by these barometric processes perfectly predicted by the barometric formula:

http://hyperphysics.phy-astr.gsu.edu/hbase/kinetic/barfor.html

Here’s some lecture slides explaining how this continuous expansion/compression by gravity do work upon the atmosphere to maintain the temperature gradient:

• Chris Barron says:

In the first tyre example, the heat is lost through conduction (contact based), not convection(movement based)

In the second example I think the heat is coming from the pump and the comparatively smaller volume of gas inside which is being worked very hard and then transferred to the tyre, rather than the pressure increase in the tyre….but then that’s just an analogy and I’m probably just being argumentative.

I didn’t fully click with the topic when I first read it this morning, got it now though.

• “In the first tyre example, the heat is lost through conduction (contact based), not convection (movement based)”

both are obviously involved:

compression of air → warming of air and then the tire rubber by conduction → rubber loses heat to the ambient air by convection.

The lecture notes I linked to and many others on adiabatic processes in the atmosphere explain how gravity is constantly doing this compression work on the adiabatic gases in the atmosphere, which is the basis of the derivation of the barometric formula, which perfectly predicts the temperatures throughout the troposphere from the pressure.

• Not pressure. Volume. Pressure at the north pole is the same as the equator, but the volume is much less, because of the temperature.

V ~ T

Tropopause at the pole is 8 kilometers, at the equator it’s 20 km.

• wayne says:

HS, do you have a reference for that claimed 83,000X figure? Or at least, to you, from where does that factor originate?

• I’ve never said any such thing.

11. kuhnkat says:

and in the winter the atmosphere cools and shrinks leaving less space between all them tiny bits for the radiation to leave making a better insulator… The fish net stockings become silk.