My OperaAEROSTATICS
Monday, June 2, 2008 7:02:42 AM
Given the density of air, a liter of gas will displace a specified amount of air, The mass displaced times the acceleration of gravity gives the buoyant force.
(liter of gas)(density of air) = (mass displaced)
(mass displaced)(acceleration of gravity) = (buoyant force per liter)
(buoyant force)/(liter) = (weight of cargo)/(volume of gas necessary)
The weight of the cargo is the weight of the balloon, the weight of the gas, and the payload.
The weight of the gas is the density of the gas times the volume of the balloon, that quantity times the acceleration of gravity.
For large payloads we can take the weight of the balloon and gas as negligible, and calculate the volume of gas needed to lift a payload. Gases such as helium are very light compared to air.
We can calculate the mass of a gas in a given volume at standard temperature and pressure, by using the fact that under such conditions the molar volume is 22.4 liters per mole, and the mass per mole of a gas is given by its molar mass as indicated in the periodic table of the elements.
The pressure of a gas is inversely proportional it its volume. We can use the ideal gas law to find the pressure of a gas needed to lift a payload knowing its volume. This is useful since some gas dispensers measure the pressure in a balloon as it is filled. The ideal gas law is:
PV=nRT
where P is pressure in atmospheres, n is moles of gas, R is the ideal gas constant equal to 0.0821 (atm)(L)/(mol) and T is temperature in degrees kelvin, V is volume in liters.
(liter of gas)(density of air) = (mass displaced)
(mass displaced)(acceleration of gravity) = (buoyant force per liter)
(buoyant force)/(liter) = (weight of cargo)/(volume of gas necessary)
The weight of the cargo is the weight of the balloon, the weight of the gas, and the payload.
The weight of the gas is the density of the gas times the volume of the balloon, that quantity times the acceleration of gravity.
For large payloads we can take the weight of the balloon and gas as negligible, and calculate the volume of gas needed to lift a payload. Gases such as helium are very light compared to air.
We can calculate the mass of a gas in a given volume at standard temperature and pressure, by using the fact that under such conditions the molar volume is 22.4 liters per mole, and the mass per mole of a gas is given by its molar mass as indicated in the periodic table of the elements.
The pressure of a gas is inversely proportional it its volume. We can use the ideal gas law to find the pressure of a gas needed to lift a payload knowing its volume. This is useful since some gas dispensers measure the pressure in a balloon as it is filled. The ideal gas law is:
PV=nRT
where P is pressure in atmospheres, n is moles of gas, R is the ideal gas constant equal to 0.0821 (atm)(L)/(mol) and T is temperature in degrees kelvin, V is volume in liters.
