Question

A sealed gas cylinder is left outside on a hot, sunny day. What happens to the average speed of the gas molecules and to the pressure of the gas in the cylinder as the temperature of the gas rises\[?\]

	Average speed of gas molecules	Pressure of gas in cylinder
A	Decreases	Decreases
B	Decreases	Increases
C	Increases	Decreases
D	Increases	Increases

\[A.\,\,\,A\]
\[B.\,\,\,B\]
\[C.\,\,\,C\]
\[D.\,\,\,D\]

Answer 1

Hint:Relation between Pressure and average speed with temperature is the main concept here. Gas pressure rises with temperature when volume is constant. The average speed of a gas molecule is also directly proportional to the temperature.

Complete step by step answer:
Among gas laws, pressure and temperature are related in Gay-Lussac’s law. According to Gay-Lussac’s law, pressure exerted by a given mass of gas is directly proportional to absolute temperature of the gas when volume is constant. The expression of Gay-Lussac’s law can be written as,
\[\dfrac{{{P_1}}}{{{T_1}}} = \dfrac{{{P_2}}}{{{T_2}}}\]
Where,
\[{P_1}\] is the initial pressure
\[{T_1}\] is the initial temperature
\[{P_2}\] is the final pressure
\[{T_2}\] is the final temperature
From the above relation we can write,
\[
  P \propto T \\
  \therefore \dfrac{P}{T} = \,constant \\
 \]
Where,
\[P\] is the pressure exerted by the gas.
\[T\] is the temperature
We can say that when pressure increases, the temperature also increases.The average speed of a gas molecule is also directly proportional to square root of temperature. It represents the kinetic-molecular theory.
It is given by the relation,
\[\mu = \sqrt {\dfrac{{8RT}}{M}} \]
\[R = \] Universal gas constant

\[{V_{av}} \propto \,{\left( T \right)^{\dfrac{1}{2}}}\]
Where,
\[{V_{av}} = \]Average speed
\[T\]\[ = \] Absolute temperature
\[M = \] Molecular mass

Therefore, it is clear that the average speed of the gas molecules and pressure of the gas molecule in the cylinder increases as temperature rises.
Therefore, the correct answer is option D.


Note:
In a sealed container the gas molecules exert a force as they collide due to random motion. It creates pressure on the container. Both the pressure and force are almost equal throughout the container. When the container is heated, the average speed rises up.