Came across this problem which I cannot figure out in Jeppesen Sanderson PHYSICS FOR AVIATION.

Here it goes:

"The air pressure and density at a point on the wing of a B 747 flying at an altitude of 2900 m are 71.0 kPa, and 0.919 kg/m^3 respectively. What is the temperature at this point on the wing in degrees Centigrade?"

I would very much appreciate the process taken to figure this problem out shown for understanding. Thank you all very much for your help!

Paul

Here it goes:

"The air pressure and density at a point on the wing of a B 747 flying at an altitude of 2900 m are 71.0 kPa, and 0.919 kg/m^3 respectively. What is the temperature at this point on the wing in degrees Centigrade?"

I would very much appreciate the process taken to figure this problem out shown for understanding. Thank you all very much for your help!

Paul

Presumably the 747 and the altitude are irrelevant? At a specified pressure and specified density the temperature is determined by them alone?

You just need the pressure and the density. If you assume that the air is ideal, and find the "molar mass" of air (about 29 g/mol, look it up online), you can just use the ideal gas law in terms of density to find temperature.

PV=nRT (where P=pressure, V=vol, n=# of moles, R=const, T=temp)

PV=(g/MM)*RT (where g is mass of gas, MM is molar mass)

P=(g/V)(RT/MM)

since g/V is density (rho),

P=rho*RT/MM

so

P*(MM) = rho*R*T

be careful with units - if you need more help, just ask again.

PV=nRT (where P=pressure, V=vol, n=# of moles, R=const, T=temp)

PV=(g/MM)*RT (where g is mass of gas, MM is molar mass)

P=(g/V)(RT/MM)

since g/V is density (rho),

P=rho*RT/MM

so

P*(MM) = rho*R*T

be careful with units - if you need more help, just ask again.

- flightsimfreak
**Posts:**698**Joined:**

It's been all summer since I've been in school, so don't crucify me if I get something wrong, just correct me.

OK, for reference, P is pressure in Pascals, T is temperature in Kelvin, D is density in Kg/m^3 and R is the ideal gas constant, or 287 K Kg/ Pa M^3. The equation I'm going to use is the Ideal gas law solved for T.

T=P/(D*R)

We know P, D, and R... So it's a simple matter now of "plug and chug" as my math teacher used to say... Plug it in to the calculator, and chug out the answer...

71.0 kPa is 71000 Pascals...

T=71000/(.919*287)

or...

269.19 K or -3.96 C

Phew, I hope I didn't mess that one up, that was a doozie

OK, for reference, P is pressure in Pascals, T is temperature in Kelvin, D is density in Kg/m^3 and R is the ideal gas constant, or 287 K Kg/ Pa M^3. The equation I'm going to use is the Ideal gas law solved for T.

T=P/(D*R)

We know P, D, and R... So it's a simple matter now of "plug and chug" as my math teacher used to say... Plug it in to the calculator, and chug out the answer...

71.0 kPa is 71000 Pascals...

T=71000/(.919*287)

or...

269.19 K or -3.96 C

Phew, I hope I didn't mess that one up, that was a doozie

Not entirely irrelevant as altitude increases, molar mass goes down a little, which means the ideal gas law will produce different numbers. At 2900m, air composition is pretty normal.

Anyway. Let's set up some variables and constants.

P = Pressure (Pascals, not atmospheres or mmHg or whatever);

D = Density;

V = Volume;

T = Temperature (Kelvin);

n = Number of moles of gas in a given volume;

R = universal gas constant (8.3144 J per mole degree)

M = Mass of a given volume of gas

Ideal gas law:*PV=nRT*

Also,*V=M/D*

So,*(P / D).(M / n) = RT*. The *(M / n)* is the value that would slowly change with altitude, or indeed if you were flying over Venus instead of Earth, but for this case we can use the typical molar mass of air, hence 28.92g/mole . R is always 8.3144 in these units.

Therefore, T = (P / D) . (3.478)

Be careful with units, significant figures, &c &c

Anyway. Let's set up some variables and constants.

P = Pressure (Pascals, not atmospheres or mmHg or whatever);

D = Density;

V = Volume;

T = Temperature (Kelvin);

n = Number of moles of gas in a given volume;

R = universal gas constant (8.3144 J per mole degree)

M = Mass of a given volume of gas

Ideal gas law:

Also,

So,

Therefore, T = (P / D) . (3.478)

Be careful with units, significant figures, &c &c

Cunning linguist

I know the ideal gas law is an approx. for air, but..

>as altitude increases, molar mass goes down a little

the mass of one mole, or 6.02e23 molecules or whatever it is should not change, no matter the state of the gas.

any two thermodynamic properties of a gas define the thermodynamic state of the gas (see http://web.mit.edu/16.unified/www/FALL/thermodynamics/thermo_2.htm for verification). In this case, density and pressure are enough.

>as altitude increases, molar mass goes down a little

the mass of one mole, or 6.02e23 molecules or whatever it is should not change, no matter the state of the gas.

any two thermodynamic properties of a gas define the thermodynamic state of the gas (see http://web.mit.edu/16.unified/www/FALL/thermodynamics/thermo_2.htm for verification). In this case, density and pressure are enough.

I guess he means the air has a higher percentage of nitrogen at higher altitudes. Which would of course lower the molar mass.

Avogadro's number does not change. The molar mass varies with the composition of the gas. This is a bit of an irrelevance, since the atmosphere is well-mixed below 80km (IE anywhere you're likely to find an airliner) so composition changes with altitude are quite small, although not always negligible.

Presuming you're dealing with the same gas at all times.

Cunning linguist

Hey Bobrayner, you're right about those two points. Hopefully he doesn't have to discuss that in his answer.

Thank you all for the input. Can we call the answer -4 c????

Paul

Paul

- PilotHighFlyer
**Posts:**217**Joined:**

This reminds me of chem...wow

No don't round to 4, keep the answer out to hundredth or thousandths for accuracy, especially if you have to use the answer in another problem.

~Robert

No don't round to 4, keep the answer out to hundredth or thousandths for accuracy, especially if you have to use the answer in another problem.

~Robert

Your answer is as accurate as the least accurate input - in this case, the pressure. Round accordingly?

Cunning linguist

Yeah, use 3 significant digits. (71.0 kPa and .919 kg/m^3 both have 3 sig figs)