1.1.  A student is investigating how the volume of an ideal gas is dependent on its temperature. A gas syringe is connected through a delivery tube to a conical flask. The gas syringe is frictionless, so that the gas pressure within the system remains equal to atmospheric pressure, p = 101 kPa. The flask is immersed in an ice bath, as shown in Figure 1. 

Figure 1

The total volume of the conical flask and delivery tube is 283 cm³, and after settling in the ice bath whilst the ice is melting, the gas syringe measures a volume of 12 cm³. 

Determine the total number of moles of the ideal gas within the flask, tube and syringe.

1.2. The ice bath is heated at a constant rate. 4 minutes are needed for the ice to melt, and then 8 minutes later, the water in the bath begins boiling. After 4 minutes of boiling, the heater is turned off. 

Determine the volume of the gas throughout the period of heating and plot a graph using the axes provided in Figure 2 below to show how the volume of the gas changes with time. 

Figure 2

1.3. The relationship between the volume of a gas and the temperature of a gas is important for hot air balloons. A hot air balloon is open at the base, so air can move in and out of the balloon. A burner at the base of the balloon is used to heat the air in the balloon, as shown in Figure 1. 

Figure 1

As the balloon rises the air pressure and air temperature around the balloon decreases. The mass of the balloon can be reduced by releasing sand from the balloon. 

Discuss the forces upon the hot air balloon due to changes in the temperature within the balloon and the changes in air pressure outside the balloon, and with reference to the ideal gas equation. In your answer you should: 

• Explain how the burner is used so the balloon can rise.

• Explain how the forces upon the balloon change with altitude and as the mass of the balloon decreases. 

You may wish to draw a diagram to clarify your answer.

The quality of your written communication will be assessed in your answer.