# Thermodynamics problem: Gas-filled cylinder & piston SHM oscillator

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1. Apr 1, 2016

### vijayramakrishnan

1. The problem statement, all variables and given/known data
An ideal gas enclosed in a vertical cylindrical container supports a freely moving piston of mass M. The piston and cylinder have equal cross sectional area A. When the piston is in equilibrium, the volume of the gas is V0 and its pressure is P0. The piston is slightly displaced from the equilibrium position and released. Assuming that the system is completely isolated from its surrounding, the piston executes a simple harmonic motion with frequency?
2. Relevant equations
fbd

3. The attempt at a solution

the solution says the process is adiabatic but i couldn't understand that,how is the process adiabatic?
how to say whether a process is adiabatic or not,if the question doesn't say that(i know what is adiabatic process)

2. Apr 1, 2016

### stevendaryl

Staff Emeritus
Why is it adiabatic? Adiabatic means that there is no heat flowing in or out of the system, and that's what they mean by saying it is isolated.

When the piston compresses the gas, the pressure goes up and the volume goes down. But if it's an adiabatic process, then the following quantity remains constant:

$P V^\gamma$

where $\gamma$ is a constant depending on the gas.

For a cylinder, the volume of the gas is just $A z$, where $A$ is the cross-sectional area and $z$ is the height of the gas in the cylinder (which is the height of the piston).

So you can relate $P$ and $V$ to the height. The force on the piston is just $F = P A$. (Because pressure is just force per unit area). So you can relate $F$ to the height, as well.

So you have a force that varies with the height $z$ of the piston. So try to figure out what that relationship is.

3. Apr 1, 2016

### vijayramakrishnan

thank you very much sir,from here i can solve it,i only didn't know,how is the process aidabatic,i missed the word.thanks once again sir.