# Ideal Gas in Cylinder with Piston (Conceptual)

• fiestyman001
In summary, the gas pressure inside the cylinder is always equilibrated by the external pressure. The entropy of the gas inside the cylinder stays the same.
fiestyman001
You have a cylinder with an ideal gas inside, enclosed by a piston. There is a valve on the side of the cylinder could let gas through if opened. The valve is then opened and some of the gas escapes slowly while maintaining thermal equilibrium. Once it is closed, the piston is a little lower than it was before. Is the final pressure of the gas inside the cylinder greater, less than, or equal to the initial pressure?

I know n, and V change, but I'm not sure if P changes..

Let me ask you this, what is causing the pressure in the cylinder?

Try a force balance on the piston, see if that answers your question.

Last edited:
fiestyman001 said:
You have a cylinder with an ideal gas inside, enclosed by a piston. There is a valve on the side of the cylinder could let gas through if opened. The valve is then opened and some of the gas escapes slowly while maintaining thermal equilibrium. Once it is closed, the piston is a little lower than it was before. Is the final pressure of the gas inside the cylinder greater, less than, or equal to the initial pressure?

I know n, and V change, but I'm not sure if P changes..

h2oski1326 observation is essential. Notice that the external forces exerted over the piston are its proper weight and the force due to atmospheric pressure. So if we assume a quasistatic process, then the internal pressure is equilibrated by the external one all the time during the process. Also to mantain thermal equilibrium (I assume, in advance, that the process is non-adiabatic as you are talking about of thermal equilibrium, but if the process were adiabatic then it is easy to show that it must be isentropic) some heat, in principle, should be transferred between the open system (control volume) and its surroundings. Furthermore, since T=const. and we are dealing with an ideal gas, the exit enthalpy may be asummed constant and equals to the system, that is h_e=C_p.T=const. But what n is? as in an isothermal process the polytropic constant is equal to 1. But I think n is the mole's number. So PV_1=m_1.R.T, and PV_2=m_2.R.T, where m_1 and m_2 are the initial and final mass resp. inside the control volume. Also by continuity eq. m_e=m_1-m_2. So by the first law of thermodynamics applied to a 'transitory' control volume
Q=m_e.h_e+m_2.u2-m_1.u_1+W,
where u_1=u_2=C_v.T, h_e=C_p.T. and W=-P(V_1-V_2), negative because work is efectued on the system by the piston.
Therefore,
Q=(m_1-m_2)C_p.T-(m_1-m_2)C_v.T-P(V_1-V_2)=(m_1-m_2)(C_p-C_v)T-P(V_1-V_2),
and we get
Q=(m_1-m_2)RT-P(V_1-V_2)=P(V_1-V_2)-P(V_1-V_2),
that is,
Q=0.
So, according to this result (and if I didn't commit mistakes), the process is also adiabatic in this very particular case. How much it is the entropy change?

## What is an ideal gas?

An ideal gas is a hypothetical gas that follows the ideal gas law, which states that the pressure, volume, and temperature of the gas are related by the equation PV = nRT, where P is the pressure, V is the volume, n is the number of moles of gas, R is the ideal gas constant, and T is the temperature. This law assumes that there are no intermolecular forces between gas particles and that the particles themselves have no volume.

## How does a gas behave in a cylinder with a piston?

In a cylinder with a piston, a gas behaves according to the ideal gas law. As the piston moves, the volume of the gas changes, causing the pressure to change as well. If the temperature remains constant, the relationship between pressure and volume is inverse (Boyle's Law). If the volume remains constant, the relationship between pressure and temperature is direct (Gay-Lussac's Law). And if the pressure remains constant, the relationship between volume and temperature is direct (Charles's Law).

## What happens to a gas when it is compressed in a cylinder with a piston?

When a gas is compressed in a cylinder with a piston, the volume decreases and the pressure increases. This is because the particles of the gas are being forced closer together, leading to more frequent collisions with the walls of the cylinder. As a result, the temperature of the gas may also increase due to the increased kinetic energy of the particles.

## Can an ideal gas ever truly exist in a cylinder with a piston?

No, an ideal gas is a hypothetical concept and does not exist in the real world. In a real gas, there are always some intermolecular forces between particles and the particles themselves have some volume. However, for most practical purposes, gases can be approximated as ideal gases under certain conditions, such as low pressure and high temperature.

## What factors affect the behavior of a gas in a cylinder with a piston?

The behavior of a gas in a cylinder with a piston is affected by several factors, including temperature, pressure, and volume. Additionally, the type of gas and the number of moles of gas present also play a role. The ideal gas law can be used to describe the relationship between these factors and how they affect the behavior of a gas in a cylinder with a piston.

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