Question

1.The dimensions or units for the quantity (Pressure * Volume) is the same as the dimensions or units of

a.force

b.energy

c.energy/temperature

d.force/temperature

2.According to the ideal gas law, PV = constant for a given temperature and amount of gas. As a result, an increase in volume corresponds to a decrease in pressure. According to the kinetic theory, this happens because the molecules

a.Collide with each other more frequently

b.Move slower on the average.

c.Strike the container wall less often.

d.Transfer less energy to the walls of the container each time they strike it.

3.An air bubble ascends from the bottom of a lake 15 m deep. The temperature at the bottom of the lake is 4oC, and near the surface it is 20oC.

Answer 1

1. b energy

2 c

3.

This problem is not a simple as it seems. I hope that you are given some additional assumptions in order to solve it. I'm going to assume that you're not supposed to use the Navier-Stokes equations and so I'll make the the assumption of ideal fluids.

Three things can change about the bubble: 1. volume, 2. pressure, 3. temperature. These are related by the ideal gas equation
P V = n k T
Where P is pressure, V is volume, n is the number of particle, k is Boltzmann's constant k = 1.38x10^(-23) joule/kelvin and T is temperature. The number of particles (n) is not going to change, and neither is k.

So we know the temperature change, but what about the pressure change. If you are to assume that the air pressure in the bubble is unchanging, then you can solve the problem as a simple ratio of temperatures using the ideal gas equation giving Vf / Vi = Tf / Ti.

However, the pressure below the surface of a liquid is given by P = P0 + p g h, where P0 is atmospheric pressure, p is the density of the liquid (water in this case), g is the acceleration of gravity and h is the depth under the surface of the liquid.

Pressure at 15 m depth = 1 + 1000 kg/m^3 * 9.8 m/s^2 * 15 m / (101325 N/m^2) = 2.45 atm

To set up the problem using this, we have

{ Pi Vi = n k Ti
{ Pf Vf = n k Tf
{ Pi = Pf + p g h

or, solved for Vf / Vi,

Vf / Vi = Tf / Ti (1 + p g h / Pf)

So now you can plug in some numbers to get (use kelvin for temps!) (Pf = 1 atm = 101325 N/m^2)

Vf / Vi = (293 K) / (277 K) * (2.45 atm/ 1 atm)

Vf / Vi = 2.59

Given Vi = 0.1 m³ Hence Vf = 2.59 * 0.1 = 0.259 m³