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DP IB Physics: HL

Topic Questions

Home / IB / Physics: HL / DP / Topic Questions / 3. Thermal Physics / 3.2 Modelling a Gas / Structured Questions


3.2 Modelling a Gas

Question 1a

Marks: 3

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.

h3ven4Pp_qu-1-a

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.
[3]
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    Question 1b

    Marks: 2
    (b)
    Calculate the surface area of the inside surface of the airship at this same point in the flight.
    [2]
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      Key Concepts
      Investigating Gas Laws

      Question 1c

      Marks: 2

      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.
      [2]
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        Key Concepts
        Ideal Gas Laws

        Question 2a

        Marks: 2

        A cylinder is fixed with an airtight piston containing an ideal gas of temperature 20 °C.

        When the pressure, in the cylinder is 3 × 104 Pa the volume, is 2.0 × 10−3 m3

        (a)
        Calculate the number of gas molecules present in the cylinder.
        [2]
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          Question 2b

          Marks: 2

          The piston is slowly pushed in and the temperature of the gas remains constant. 

          (b)
          Draw a graph by plotting three additional points on the axis to show the relationship between pressure and volume as the piston is slowly pushed in. 

          qu-2-a
          [2]
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            Key Concepts
            Investigating Gas Laws

            Question 2c

            Marks: 2

            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. 

            3-2-ib-sl-hard-sq-2c-q

            Cylinder X is pushed down by a distance Δhx causing Y to move up a distance Δhy. The pressure and temperature within the system both remain constant. 

            (c)
            Determine the ratio Δhx : Δhy.
            [2]
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              Key Concepts
              Ideal Gas Laws

              Question 2d

              Marks: 5

              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.
              [2]
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                Key Concepts
                Investigating Gas Laws

                Question 3a

                Marks: 2

                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.  

                qu-3-a

                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.
                [2]
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                  Key Concepts
                  Mole Calculations

                  Question 3b

                  Marks: 3

                  When the ice bath is heated at a constant rate it takes the following time to melt the ice and heat the water:

                  • Time for ice to melt is 3 minutes
                  • Time from ice melting to water boiling is 10 minutes
                  • Time for water to boil is 3 minutes
                  (b)
                  (i)
                  Calculate the volume of the gas at its boiling point.
                  [1]
                  (ii)
                  Sketch a graph to show this process.

                  qu-3-b
                  [2]
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                    Key Concepts
                    Ideal Gas Laws

                    Question 3c

                    Marks: 6

                    A burner in the base of a hot air balloon is used to heat the air inside the balloon. 

                    Xg2friXs_qu-3-c

                    The mass of the balloon can be reduced by releasing sand from the basket of the balloon. 

                    (c)
                    (i)
                    Explain how the burner is used so the balloon can rise.
                    [3]
                    (ii)
                    Explain how the forces on the balloon change with altitude and as the mass of the balloon decreases.
                    [3]
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                      Question 4a

                      Marks: 2

                      A sealed container C has the shape of a rectangular prism and contains an ideal gas. The dimensions of the container are land h

                      rQpCK2bw_qu-5-a

                      • The average force exerted by the gas on the bottom wall of the container is F
                      • There are moles of gas in the container
                      • The temperature of the gas is 
                      (a)
                      Obtain an expression in terms of F, and for the height of the container.
                      [2]
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                        Question 4b

                        Marks: 2

                        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 cylinder D is 600 K. 

                        (b)
                        Calculate the temperature of cylinder D in °C.
                        [2]
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                          Key Concepts
                          Ideal Gas Equation

                          Question 4c

                          Marks: 3

                          The temperature of a different container 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.
                          [3]
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                            Key Concepts
                            Ideal Gas Equation

                            Question 4d

                            Marks: 2

                            In a different container F the pressure of the gas is measured at different temperatures whilst the volume and number of moles are kept the same. 

                            (d)
                            Plot a graph to show how the pressure varies with temperature for this gas.
                            qu-5-d
                            [2]
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                              Key Concepts
                              Ideal Gas Laws