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A bubble of air is at the bottom of a water tank 15 cm deep. If the atmospheric pressure is 1.3 x 105 Pa, calculate: (i) the pressure at the bottom of the tank. (ii) If the bubble has a volume of 1.2

Physics

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  1. Answer Question 1 (c) i.

    To determine the pressure at the bottom of the water mass, we use the formula for hydrostatic pressure.
    Given:
    Density of water ρ=1000kg m−3\rho = 1000 \text{kg m}^{-3}
    Depth h=15cm=0.15mh = 15 \text{cm} = 0.15 \text{m}
    Atmospheric pressure Patm=1.3×105PaP_{atm} = 1.3 \times 10^5 \text{Pa}
    Acceleration due to gravity g=9.8m s−2g = 9.8 \text{m s}^{-2}

    The pressure at the bottom of the water mass is the sum of the atmospheric pressure and the pressure due to the water column:

    Pbottom=Patm+ρghP_{bottom} = P_{atm} + \rho g h Pbottom=1.3×105Pa+(1000kg m−3×9.8m s−2×0.15m)P_{bottom} = 1.3 \times 10^5 \text{Pa} + (1000 \text{kg m}^{-3} \times 9.8 \text{m s}^{-2} \times 0.15 \text{m}) Pbottom=1.3×105Pa+1470PaP_{bottom} = 1.3 \times 10^5 \text{Pa} + 1470 \text{Pa} Pbottom=130000Pa+1470PaP_{bottom} = 130000 \text{Pa} + 1470 \text{Pa} Pbottom=131470PaP_{bottom} = 131470 \text{Pa}

    The pressure at the bottom of the water mass is 1.3147×105Pa\boxed{\text{1.3147} \times 10^5 \text{Pa}}.

  2. Answer Question 1 (c) ii.

    To determine the volume of the bubble at the surface, we use Boyle's Law, assuming the temperature remains constant.
    Given:
    Pressure at bottom Pbottom=131470PaP_{bottom} = 131470 \text{Pa} (from part i)
    Volume at bottom Vbottom=1.2×10−6m3V_{bottom} = 1.2 \times 10^{-6} \text{m}^3
    Pressure at surface Psurface=Patm=1.3×105PaP_{surface} = P_{atm} = 1.3 \times 10^5 \text{Pa}

    Boyle's Law states: PbottomVbottom=PsurfaceVsurfaceP_{bottom} V_{bottom} = P_{surface} V_{surface}

    Vsurface=PbottomVbottomPsurfaceV_{surface} = \frac{P_{bottom} V_{bottom}}{P_{surface}} Vsurface=131470Pa×1.2×10−6m31.3×105PaV_{surface} = \frac{131470 \text{Pa} \times 1.2 \times 10^{-6} \text{m}^3}{1.3 \times 10^5 \text{Pa}} Vsurface=157764×10−6m3130000V_{surface} = \frac{157764 \times 10^{-6} \text{m}^3}{130000} Vsurface=1.213569×10−6m3V_{surface} = 1.213569 \times 10^{-6} \text{m}^3

    The volume of the bubble at the surface is 1.21×10−6m3\boxed{\text{1.21} \times 10^{-6} \text{m}^3}.

  3. Answer Question 13 (a).

    The freezing chamber in a refrigerator cannot be placed at the bottom because cold air is denser than warm air. For efficient cooling, the cold air produced by the freezer needs to sink and circulate throughout the entire refrigerator compartment. If the freezer were at the bottom, the cold air would remain there, and the upper parts of the refrigerator would not be cooled effectively due to poor convection.

  4. Answer Question 13 (b).

    The specific latent heat of vaporization is the amount of heat energy required to change a unit mass of a substance from its liquid state to its gaseous state at a constant temperature and pressure. This energy is used to overcome the intermolecular forces in the liquid, not to increase the kinetic energy of the molecules.

  5. Answer Question 13 (c).

    When steam is introduced into a room and condenses, it changes from a gaseous state to a liquid state. During this phase change, the steam releases its latent heat of vaporization into the surroundings. This released heat energy increases the internal energy of the air molecules in the room, leading to an observable rise in the room's temperature.

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