To calculate the molar densities from the weather balloon measurements, we converted all of the pressures and temperatures into units of Pa and K, and then determined the values at each pressure using D = n / V =P / RT, where R is
the ideal gas constant (8.314 J / K / mol)
T = temperature p = pressure V = olume R =
ideal gas constant Cp = ideal gas heat capacity = 5 / 2R g = gravitational constant rho = density = 1 / V z = vertical spatical coordinate.
n is the number of moles of gas in question and R is
the ideal gas constant.
Not exact matches
For example any (
constant) volume of
ideal gas at room temperature (20 °C) increases its pressure by a factor fo 4.3 when heated to 1000 °C.
Since this commercial space is set in an
ideal and well known location, alongside the San Cas Warehouse and other business establishments such as Atlantic Bank,
gas stations, Bowen & Bowen Ltd, schools it provides the added benefit of
constant clientele.
The
gas on the bottom behaves like an ordinary
ideal gas, after all, and expands when warmed at
constant pressure.
c) It is completely irrelevant to the discussion at hand, involving a simple
ideal gas in an ordinary vertical column with
constant g.
If we assume a
constant temperature in the adiabatically isolated container, one gets the following formula for the density of an
ideal gas:
The
gas at the top of the tube would be warmed (thus increasing its pressure slightly (
ideal gas laws temperature change
constant volume tube) and like a piston this pressure increase would propagate down the tube at the local speed of sound in the
gas causing adiabatic heating of the
gas in each subsequent layer until it reached the bottom of the tube, instantly replacing the heat lost to the silver wire.
Nor is pressure
constant in a gravitationally bound column of
ideal gas.
So if one uses the heat engine to do external work, the
gas in the cylinder will indeed drop to zero in temperature as all of its internal energy drops to the bottom to maintain a
constant temperature difference right up to where the temperature of the
ideal gas at the top reaches zero.
where g is the gravitational acceleration (presumed approximately
constant throughout the spherical shell) and cp is the heat capacity per kilogram of the particular «
ideal»
gas at
constant pressure.
The
constant speed moving parcel of the
ideal gas is the same solution as still air for hydrostatic equilibrium.
According to the
ideal gas law PV = nRT, additional warmth (increased T) reduces density when P is held
constant, namely by increasing V while leaving n (the number of moles and hence the mass) unchanged.
Furthermore the volume V = NkT / P should stay more or less
constant since k and P are
constant while NT (product of number N of molecules with temperature T) should also remain roughly
constant because although N has decreased very slightly, this is offset by the corresponding slight increase in T. (This is how I would address Eli's concern that condensation violates the
ideal gas law.)
We generally believe that the standard notations that introduce a
gas - specific
constant to the
ideal gas law are misleading.
Increase the temperature of an
ideal gas and the pressure and / or volume increases (assuming a
constant amount of
gas).
Given the
ideal gas law, and the fact that the flask contains a
constant volume, that means the increase in pressure for pure CO2 would in the flask would result in less than a 2.6 x10 ^ -6 oC increase in temperature.
Also, this is
ideal gas «
constant rapid motion» by which it means travelling at great speeds through empty space, it does not mean the vibrational movement of the molecule which is anyway confined by by the other real
gas molecules under gravity around it.