1A How Does Kinetic Molecular Theory Explain Why

Question

1a. How does kinetic molecular theory explain why pressure is directly propirtional to temperature at a fixed volume? 1b. Explain Boyle’s Law using the Kinetic Molecular Theory. 1c. A hot air balloo…

1a.
How does kinetic molecular theory explain why pressure is directly
propirtional to temperature at a fixed volume?

1b. Explain Boyle’s Law using the Kinetic Molecular
Theory.
1c. A hot air balloonist is rising too fast for her liking.
should she increase or decrease the temperature of the gas in the
balloon?
1d. Could the pilot of the balloonist from (1c) reduce her
rate of ascent by allowing some gas to leak out of the
balloon?

Solutions

Expert Solution

1a) Gas pressure is due to the collision of gas particle with
the walls of the container. We know that the average kinetic energy
of a molecule directly proportional to its temperature. As a result
if temperature increases the speed in which the gas molecules hit
the wall increases and leads to greater collision. Finally the
pressure of the system will increase.

1b) At constant temperature if there is an increase in pressure
results in the expansion of a gas molecules. Because the average
kinetic energy of the gas particle is increased by keeping the
temperature constant it has to expand to accommodate the changes in
the system. Therefore according to kinetic molecular theory at
constant temperature pv= constant.

1c) If the balloon is rising too fast then the temperature of
the gas in the balloon should be decreased in order to reduce its
average kinetic energy. Hot air is weighs less than the same amount
of cold air and the difference in density helps the balloon to
rise.

1d) it is not a proper way to control the rate of ascent by
allowing gas to leak out of the balloon. We can control the
buoyancy by reducing the temperature of lifting gas and there by
more controlled and safe journey.


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