Answer [1]: No, the temperature will not triple. When the speed of each molecule is tripled then the root-mean-square velocity will also triple. Consequently, the kinetic energy of each molecule will increase by a factor of 9. Therefore, the Kelvin temperature of the gas will also increase by a factor of 9.
Answer [2]: No, the kinetic energy will not double. In fact, the kinetic energy is related to the absolute temperature through the relationship:
So, if the Celsius temperature increases from 50°C to 100°C, the absolute temperature (or Kelvin temperature) increases from 323K to 373K. Thus, the fractional increase in kinetic energy is (373/323) ~ 1.15.
Answer [3]: According to the kinetic theory the energy of N molecules of an ideal gas at a (Kelvin) temperature T is (3/2)NkBT. Thus, the energy depends only on the temperature. So, if the pressure and volume are changed isothermally there will be no change in internal energy. This means that the changes in pressure (P) and volume (V) have to be such that the product PV remains constant, i.e., if you double the pressure you must halve the volume.
Answer [4]: If the rms speed are the same then the argon atoms have the greater kinetic energy, because the mass of argon atoms is about 10 times that of helium atoms. Since the (absolute) temperature of an ideal gas is directly proportional to the kinetic energy of the atoms then the temperature of the container of argon atoms (in Kelvins) is about 10 times that of the container of helium atoms.
Answer [5]: When the bottle is very full, the volume of air in the bottle above the wine is relatively small. Consequently, when the cork is inserted the reduction in volume that occurs is an appreciable fraction of the original volume. Thus, there is a correspondingly large increase in pressure, which may be sufficient to push the cork out. If some of the wine is removed, the volume of air above the wine is now much larger and so the relative reduction in volume when the cork is pushed in is now much smaller. As a result, the increase in pressure is much smaller and not sufficient to push the cork out.
Answer [6]: The pressure of the gas on the walls of the container is due to the force that occurs when the molecules rebound; we know from the impulse-momentum relationship that the force (F) is given by:
where t is the time of collision, m is the mass and vi and vf are the initial and final velocities of the molecule, respectively. If the collision is elastic:
so
If the final speed is less than the initial speed then the force, F, will be smaller and, as a result, the pressure will be less than that predicted by the kinetic theory.
Answer [7]: Yes, as bubbles rise from the bottom of a glass their volume (size) increases! Why? ... because as a bubble rises it experiences decreasing hydrostatic pressure (see Chapter 13). The gas laws tell us that, assuming the beer is at constant temperature, the product of the pressure and volume must be constant also. As a result, the reduction in pressure on the bubble will lead to an increase in volume.
However, the effect of the change in pressure on volume is actually very small in the case of beer in a glass. A much larger effect is the increase in volume due to an increase in the number of molecules of gas in the bubble! Why is that? ... because a bubble acts as a "nucleation" (or "birth") point for other bubbles; they quickly merge to form a larger bubble.
But what about the speed of a bubble as it rises? The speed will increase also because the increase in volume leads to an increase in the upthrust on the bubble ... remember, the upthrust is equal to the weight of beer displaced, which increases as the volume of the bubble increases.
Answer [8]: One mole of any substance contains Avagadro's number (6.02 ¥ 1023) of particles. Consequently, one mole of hydrogen and one mole of oxygen contain the same number of molecules.
Since they both contain the same number of molecules and the mass of an oxygen molecule is about 16 times that of a hydrogen molecule, one mole of oxygen has about 16 times the mass of one mole of hydrogen.
Answer [9]: Yes, the kinetic energy of the individual molecules does increase but the total energy does not, at least not proportionally. When you heat the air in the room, the volume of the room doesn't change (if it does it is essentially negligible) so neither does the volume of air! Perhaps a little less obvious is that the pressure doesn't change either ... the room is not sealed and so, since the pressure inside the room must be same as the pressure outside, any increase in pressure in the room will result in air molecules "leaking" out. As a result, the pressure (P) and volume (V) of air in the room remains the same, therefore, the product PV is constant. Since:
the total energy does not increase since the number of molecules decreases! Neat, huh?
Of course, we have assumed that air is an ideal gas.