Gas cylinder at constant pressure being exposed to atmosphere, how?

In summary: there is a simplification in the textbook's explanation of how the gas maintains atmospheric pressure when the piston moves, which is that atmospheric pressure is constant.
  • #1
bruhtation
1
0
TL;DR Summary
a figure in a textbook shows a cylinder filled with gas and one side of the cylinder has a movable piston which is open to the atmosphere, the textbook says "This ensures the gas in the cylinder is always at a constant pressure". how did the book deduce that?
im learning thermodynamics and currently in a lesson about thermal processes. one process has constant pressure and before diving into equations or any proof the book provides a figure of a gas cylinder. the cylinder has a movable piston/lid on one side. the book then says "...and the piston end of the cylinder is open to the atmosphere. This ensures that the gas in the cylinder is always at a constant pressure."
how was the book able to deduce that the cylinder had constant pressure just by the fact that it's piston is exposed to the atmosphere?

i dont know if this is relevant but the book talks about hot-air balloons and pressure in the previous paragraph:
"If you've ever seen a large hot-air balloon being inflated, then you know that the gas in the balloon expands as it is heated. The balloon is surrounded by the atmosphere as it is heated, and the atmosphere is at a constant pressure. Therefore, the heating and expansion of the balloon occur with no change in pressure."
i really didnt understand this part so if anyone can help me out with this too i would really appreciate it.
 
Science news on Phys.org
  • #2
In order to pressurize a container different from atmospheric it has to be rigid or otherwise inhibit expansion and contraction. If the balloon were closed and you heated it, the pressure would go up.
 
  • #3
bruhtation said:
how was the book able to deduce that the cylinder had constant pressure just by the fact that it's piston is exposed to the atmosphere?
If air pressure > cylinder gas pressure, piston moves inward until they have same pressure.
If air pressure < cylinder gas pressure, piston moves outward until they have same pressure.
 
  • #4
bruhtation said:
TL;DR Summary: a figure in a textbook shows a cylinder filled with gas and one side of the cylinder has a movable piston which is open to the atmosphere, the textbook says "This ensures the gas in the cylinder is always at a constant pressure". how did the book deduce that?

how was the book able to deduce that the cylinder had constant pressure just by the fact that it's piston is exposed to the atmosphere?
If the pressure inside the cylinder is greater than atmospheric pressure, the force exerted by the gas on the piston will be greater than the force due to atmospheric pressure on the piston, making the piston move (the gas will expand) until the forces are balanced, meaning that the pressures are equal (since pressure is simply average force per unit area). Note that one usually considers a simplified model, where things like the weight of the piston or its friction against the cylinder are neglected.

Similarly for the balloon. Note however that this is not true of a rubber balloon, where some of the internal pressure is compensated in part by the tensile force of the balloon itself. The pressure inside is then greater than atmospheric pressure.
 
  • Like
Likes russ_watters and Lord Jestocost
  • #5
Not sure if this is what is tripping you up. There is a hidden assumption (really, more of a simplification) in here that - for the purposes of the scenario - atmospheric pressure is constant.

When the piston moves, in response to expansion and contraction of the gas, this allows the gas to always maintain atmospheric pressure.
 
  • Like
Likes russ_watters
  • #6
bruhtation said:
The balloon is surrounded by the atmosphere as it is heated, and the atmosphere is at a constant pressure. Therefore, the heating and expansion of the balloon occur with no change in pressure.
The internal and external pressures are only the same at the bottom opening of a hot air balloon. Hydrostatic pressure falls as you rise, at a rate proportional to density. The air inside the balloon is less dense, so the pressure falls slower inside the envelope than in the atmosphere outside. In the upper parts of the balloon, there is a greater internal hydrostatic pressure remaining than there is outside. That differential pressure lifts the envelope, and so the balloon.
 
  • #7
DaveC426913 said:
Not sure if this is what is tripping you up. There is a hidden assumption (really, more of a simplification) in here that - for the purposes of the scenario - atmospheric pressure is constant.

When the piston moves, in response to expansion and contraction of the gas, this allows the gas to always maintain atmospheric pressure.
The pressure of the gas inside the cylinder is equal to atmospheric pressure PLUS the pressure exerted by the piston in response to gravity.
 
  • #8
Please write down the Newton's 2nd law force balance equation for the piston as a free body, letting ##F_g## represent the force that the gas exerts on the piston during the process.
 
  • #9
Hillbillychemist said:
The pressure of the gas inside the cylinder is equal to atmospheric pressure PLUS the pressure exerted by the piston in response to gravity.
That kind of depends on the piston's weight, location and orientation, don't it? 🤔 And one of that is specified.Regardless, we are explicitly told to ignore it:
"Note that one usually considers a simplified model, where things like the weight of the piston or its friction against the cylinder are neglected."
 

Similar threads

Replies
5
Views
727
Replies
3
Views
1K
Replies
56
Views
3K
  • Thermodynamics
Replies
20
Views
2K
Replies
14
Views
787
Replies
22
Views
2K
  • Introductory Physics Homework Help
Replies
8
Views
786
  • Mechanical Engineering
Replies
3
Views
1K
Replies
7
Views
1K
Replies
7
Views
893
Back
Top