# Ideal gas in a cylinder closed by a piston connected to a spring

• amcca064
In summary, the conversation discusses a problem involving a closed cylinder with a piston connected to a spring and filled with gas. The pressure, temperature, and volume of the gas are given and the task is to determine the height of the piston and the pressure of the gas when the temperature is increased. The solution involves using the ideal gas law, the concept of equilibrium, and the relationship between pressure and volume. The final answers are a piston height of 0.930m and a gas pressure of 186000 Pa.
amcca064
A cylinder is closed by a piston connected to a spring of constant 2.00 X 10^3 N/m. With the spring relaxed, the cylinder is filled with 5.00L of gas at a pressure of 1.00 atm and a temperature of 20.0ºC. A) If the piston has a cross-sectional area of 0.0100 m^2 and neglible mass, how high will it rise when the temperature is raised to 250º? b) What is the pressure of the gas at 250º?

This whole question has me stumped, at first I thought it would be simple ideal gas law question, but then I thought about the force of the spring back on the gas and how that would affect pressure. The way I have it so far is net force on the piston in the direction of the spring if the cylinder is vertical with the end sealed by the piston at the top (y axis) is F = -Fs + [P(gas) X A(piston)] at 20ºC system is in equilibrium so kh = P(gas) X A(piston) ---> h = [P(gas) X A(piston)] /k ---> h=(101300Pa X 0.0100m^2)/(2.00 X 10^3 N/m) =0.507m Does this seem right? I don't even think I'm on the right track here... any help would be great thanks!

In both the initial state and the final state the piston is in equilibrium. but in the beginning there's the same amount of pressure on the top and on the bottom of the piston (1) and so the spring is relaxed - the force of the spring is 0 (h=0). but when the gas is heated then there's more pressure inside so in order to be in equilibrium the spring has to push harder, this means that the spring has to move up so that it pushes more (f=k*x).
and don't forget that as the piston goes up the volume gets bigger and the pressure goes down so the pressure is also a function of h.

Ok thanks, that was another way I looked at doing it but I made some serious mistakes when I laid out my eqs... what I have this time is P=F/A and since spring is in equilibrium with force exerted by the gas... P=kh/A
Volume = A X h so P1V1/T1 = P2V2/T2 ---> [(101300Pa)(5.00m^3)] / 293K = [(kh/A) X (A X h)] / 543K ---> 1730 = k X h^2 h=0.930m I think this works out or is V2 = 5.00 + (AXh)?? then for the pressure, its simply hk/A = 186000 Pa

V2 = 5.00 + (AXh) because in the initial condition h=0 and V=5.
and also, in the final state P=kh/A + 1 because the pressure in the container also has to push against the pressure outside the container - you know this cause in the initial state there was no force on the spring but there was pressure of 1atm in the cylinder.

Ok awesome thanks so much!

hi, it seems we have got the same problem.well, i am new in this area so,i am afraid of that i couldn't understand.could you let me see the answer step by step...such as like...

a)
b)

thanks...

Thanks for the jump start-- 5 L is not equal to 5 m^3 though. 1000 Liters is 1 m^3

## 1. What is an ideal gas?

An ideal gas is a theoretical gas that follows the gas laws perfectly under all conditions. It is assumed to have no intermolecular forces and its particles are considered to be point masses with no volume.

## 2. What is a cylinder closed by a piston?

A cylinder closed by a piston is a container that holds the ideal gas and has a movable piston at one end. The other end is sealed and does not allow gas to escape.

## 3. How is a piston connected to a spring in an ideal gas setup?

The piston is connected to the spring by a rod or shaft. When the gas molecules collide with the piston, they exert a force on it, causing it to compress the spring. The spring then exerts an equal and opposite force on the piston, keeping it in equilibrium.

## 4. What is the purpose of a spring in an ideal gas setup?

The spring serves as a restoring force, ensuring that the piston stays in equilibrium and exerts a constant pressure on the gas inside the cylinder. It also allows for changes in volume as the gas expands or contracts.

## 5. How does the ideal gas law apply in this setup?

The ideal gas law, PV = nRT, applies to this setup as it describes the relationship between pressure (P), volume (V), number of moles (n), and temperature (T) for an ideal gas. In this setup, the volume and pressure can be changed by adjusting the position of the piston, while the temperature and number of moles remain constant.

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