Chapter U3.60, Problem 3E

Interpretation Introduction

Interpretation: The information regarding the increase in pressure of gas in a cylinder is given. The reason for this change has to be explained.

Concept introduction: Pressure is defined as the amount of force that acts over one unit of area. It is exerted by one substance over other substance. Molecules of the gas are in constant motion. This motion leads to the pressure over the walls of the container.

Answer to Problem 3E

The increase in pressure of gas in a cylinder occurs due to increased temperature of the gas or decrease in volume of the gas present in the sample.

Explanation of Solution

According to Boyle’s law, pressure and volume are inversely related to each other by relation shown below.

  $PV=\text{K}$

Now, if the pressure of the gas is decreased then molecules will collide more frequently with each other as well as with walls of the container. During collision of molecules force is exerted on each other and this ultimately leads to an increased pressure.

According to Gay Lussac’s law, at the conditions of constant volume and constant number of particles, the relationship between pressure and temperature of gas is given as shown below.

  $P=\text{constant}\times T$

Thus, both pressure and temperature are directly proportional to each other. Now, when the gas temperature is increased then the kinetic energy of the molecules will also increase. This will lead to an increase in collision of molecules with the walls of the container as well as among each other. Thus, pressure exerted by gas molecules increases.

Conclusion

The increase in pressure of gas in a cylinder occurs due to increased temperature of the gas or decrease in volume of the gas present in the sample.