Adiabatic compression of piston and finding the velocity ratio of gas

Oct 10, 2023

litmusgod

TL;DR Summary: I am solving a problem related in finding the velocity ratio of gas molecules just after and before piston during adiabatic compression.
High pressure Gas is pumped from a vessel to a chamber consisting of piston and other side diaphragm is placed which will break at certain pressure .I was trying to find the velocity ratio of gas molecules after and before piston during compression and in different scenarios like Air -Air , Helium -Helium and Helium - Air respectively in vessel and chamber .

But when I solved, Air-Air is coming with highest velocity ratio than the others, which cannot be possible as helium - air and helium- helium is supposed to be faster.
I will attach the picture of the formula i used . It's work equation . So basically during equilibrium state the pressure acting on both side will be equal so i considered as equal work . From there i calculated it .

F is the force acting on piston
N is the number of the molecules of the gas enclosed in the cylinder.
m - mass of gas
c - velocity of molecules at temp T
v - velocity of the movement of piston
N is calculated using PV/RT with temperature as 298K

How does the adiabatic process differ from an isothermal process?

In an adiabatic process, no heat is transferred into or out of the system, causing changes in temperature and pressure solely due to work done on or by the gas. In contrast, an isothermal process maintains a constant temperature by allowing heat exchange with the surroundings, meaning any work done results in heat flow to keep the temperature stable.

What is the adiabatic condition for an ideal gas?

The adiabatic condition for an ideal gas is described by the equation \( PV^\gamma = \text{constant} \), where \( P \) is the pressure, \( V \) is the volume, and \( \gamma \) (gamma) is the adiabatic index or ratio of specific heats ( \( C_p / C_v \) ). This relationship implies that as the gas is compressed or expanded adiabatically, the product of pressure and volume raised to the power of \( \gamma \) remains constant.

How can you calculate the final temperature of a gas after adiabatic compression?

The final temperature after adiabatic compression can be calculated using the equation \( T_f = T_i \left( \frac{V_i}{V_f} \right)^{\gamma - 1} \), where \( T_f \) is the final temperature, \( T_i \) is the initial temperature, \( V_i \) is the initial volume, \( V_f \) is the final volume, and \( \gamma \) is the adiabatic index.

What is the velocity ratio of gas in adiabatic compression, and how is it determined?

The velocity ratio of gas in adiabatic compression refers to the relationship between the initial and final velocities of gas particles. It can be determined using the principles of conservation of energy and the adiabatic condition. The ratio can be expressed as \( \left( \frac{v_f}{v_i} \right) = \left( \frac{T_f}{T_i} \right)^{1/2} \), where \( v_f \) and \( v_i \) are the final and initial velocities, respectively, and \( T_f \) and \( T_i \) are the final and initial temperatures.

Adiabatic compression of piston and finding the velocity ratio of gas

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Related to Adiabatic compression of piston and finding the velocity ratio of gas

What is adiabatic compression in the context of a piston?

How does the adiabatic process differ from an isothermal process?

What is the adiabatic condition for an ideal gas?

How can you calculate the final temperature of a gas after adiabatic compression?

What is the velocity ratio of gas in adiabatic compression, and how is it determined?

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