# Calculating Final Pressure of an Adiabatic Gas Expansion

• fiziks09
In summary, the conversation discusses a homework problem involving an adiabatic expansion of a monoatomic gas. The first part of the problem is solved using the first law of thermodynamics and the state equation for an adiabatic process. However, there is difficulty in solving for the final pressure, which requires knowledge of the quotient of heat capacities. After some discussion, it is determined that the quotient of heat capacities for a monoatomic gas is 1.667 and further calculations are needed to solve for the final pressure.
fiziks09

## Homework Statement

As a 1.00 mol sample of a monoatomic gas expands adiabatically the work done on it is
-2.50x10^3J. The initial temperature and pressure of the gas are 500k and 3.60atm. Calculate
a. The final temperature and b. The final pressure.

## Homework Equations

First law of thermodynamics
Eint = Q + W

## The Attempt at a Solution

I was able to solve the first part of the question. Since it was an adiabatic process Q = 0 and then used Eint = nCv(Tb - Ta) to get the final temperature which is 300k.

But i can't seem to get the final pressure. I have no idea on how to begin. Please any help will be very much appreciated.

Use the state equation for an adiabatic process i.e. p*T^(k/(1-k))=constant. Where k is the quotient of the heat capacities.

quotient of heat capacities?? please i don't understand that part!

Its just that k=C_p/C_v. The quotient of the heat capacities at constant pressure and constant volume.

okay..i get that part.. is the constant R??

No... that equation means that this quantity p*T^(k/(1-k)) is constant throughout the process. Which means that its the same in the beginning and at the end. U know the pressure and temperature at the beginning you know tht temp at the end...

ok.. but I'm getting a wrong answer which is 5.9atm but it should be 1atm...

Are you making your calculations correctly? what's the value you got for k for the gas?

i got 1.5
i used C_v to be 3/2R since the gas is monoatomic and C_p to be 5/2R

shouldnt it be 1.667? And then what's the next step? show the whole calculation otherwise i can't see wtz wrong...

## What is the formula for calculating final pressure?

The formula for calculating final pressure is P1V1 = P2V2, where P1 and V1 represent the initial pressure and volume, and P2 and V2 represent the final pressure and volume.

## How do you convert from Celsius to Kelvin for use in the ideal gas law?

To convert from Celsius to Kelvin, simply add 273.15 to the Celsius temperature. This will give you the temperature in Kelvin, which is necessary for use in the ideal gas law.

## What units should be used for pressure and volume in the ideal gas law?

For the ideal gas law, pressure should be in atmospheres (atm) and volume should be in liters (L). However, if other units are used, they can be converted to atm and L as long as they are consistent throughout the equation.

## Can the ideal gas law be used for all types of gases?

The ideal gas law can be used for most gases at low pressures and high temperatures. However, it may not be accurate for gases that deviate significantly from ideal behavior, such as polar gases or gases at very high pressures.

## What happens to final pressure if the initial volume is decreased while the initial pressure remains constant?

If the initial volume is decreased while the initial pressure remains constant, the final pressure will increase. This is because the volume and pressure have an inverse relationship according to Boyle's Law.

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