(a) show that the pressure exerted by a fluid P (in pascals) is given by P= hdg, where h is the column of the fluid in metres, d is density in kg/m3, and g is the acceleration due to gravity (9.81 m/s2). (Hint: see appendix 2.). (b) The volume of an air bubble that starts at the bottom of a lake at 5.24 degree celsius increases by a factor of 6 as it rises to the surface of water where the temperature is 18.73 degree celsius and the air pressure is 0.973 atm. The density of the lake water is 1.02 g/cm3. Use the equation in (a) to determine the depth of the lake in metres.

56.4 m

Explanation:

volume increases by factor of 6, i.e = 6

Initial temperature T1 at bottom of lake =  5.24°C = 278.24 K

Final temperature T2 at top of lake = 18.73°C = 291.73 K

NB to change temperature from °C to K we add 273

Final pressure P2 at the top of the lake = 0.973 atm

Initial pressure P1 at bottom of lake = ?

Using the equation of an ideal gas

=

P1 = =

P1 = 5.57 atm

5.57 atm = 5.57 x 101325 = 564380.25 Pa

Density Ρ of lake = 1.02 g/ = 1020 kg/

acceleration due to gravity g = 9.81

Pressure at lake bottom = pgd

where d is the depth of the lake

564380.25 = 1020 x 9.81 x  d

d = = 56.4 m

it can be observed without changing the identity of the object.

it depends on what substance you're talking about as well as many other factors. in quantum mechanics, the observation of particles affects the observers ability to measure certain properties. for example: you can know the velocity of a particle, but you can't know it's position; or you can know it's position, but not it's velocity. it's like trying to find out where a grain of sand is by throwing other grains of sand at it. once you find out where it is, it's been moved. it's also like trying to find an answer to the question of whether or not a tree falling in a forest makes a sound if nobody is there to hear it. paradoxically, the only way to find out is to be there and hear it.