An airship floats in air due to a balance of weight and buoyancy forces. The buoyancy force is equal to the weight of the air that would have taken up the space that the airship occupies.
At one point in the flight, the helium gas has a temperature of 12 °C and a mass of 1350 kg. The mass of the airship materials is 6970 kg.
Air has a density of 1.225 kg m−3 and the atomic mass of helium is 4 g mol−1.
(a)
Calculate the pressure in the airship at this point in the flight.
The pressure within the airship remains constant as the material surrounding the airship is able to expand and contract when the gas inside changes temperature.
(c)
Determine the temperature, in °C, at which the airship could maintain a constant height.
The cylinder, cylinder X is connected now to a second cylinder, cylinder Y which is initially fully compressed. Cylinder Y has a diameter two times that of the diameter of cylinder X. The total number of molecules in the system remains the same.
Cylinder X is pushed down by a distance Δhxcausing Y to move up a distance Δhy. The pressure and temperature within the system both remain constant.
Initially, the gas molecules are divided between both cylinders. The diameter, d, of cylinder X, is 16 cm. The piston in cylinder X is compressed at a constant rate until all of the gas is moved into cylinder Y over a period of 5 seconds.
Assume that the volume of the connecting tube is negligible.
(d)
(i)
Sketch and label a graph to show how the length of the cylinder Y, hy changes with time.
[3]
(ii)
Calculate the power exerted during the compression.
A gas syringe is connected through a delivery tube to a conical flask, which is immersed in an ice bath. The syringe is frictionless so the gas pressure within the system remains equal to the atmospheric pressure 101 kPa.
The total volume of the conical flask and delivery tube is 275 cm3, and after settling in the ice bath whilst the ice is melting the gas syringe has a volume of 15 cm3.
(a)
Calculate the total number of moles contained within the system.
A second container D contains the same ideal gas. The pressure in D is a fifth of the pressure in C and the volume of D is four times the volume of C. In D there are three times fewer molecules than in C.
The temperature of a different container E is 60 °C. At this temperature, the pressure exerted by the ideal gas is 1.75 × 105 Pa. The container is a cube and has a height of 4 cm.
(c)
Calculate the number of molecules of gas in this container.
