Ideal diatomic gas undergoing adiabatic compression

The initial pressure and volume were given, as well as the final pressure. Chetan attempted to solve the problem using the equation ΔU=5/2*(P2V2-P1V1), but was unsure of the initial volume. Another user suggested using the differential form of the equations and integrating with the ideal gas law.
  • #1
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Homework Statement



A very simple question, but I can't figure it out.
An ideal diatomic gas, with rotation but no oscillation, undergoes an adiabatic compression. Its initial pressure and volume are 1.20 atm and 0.200 m^3. Its final pressure is 3.60 atm. How much work is done by the gas?

Homework Equations



Adiabatic, so Q=0 and ΔEint=W (because it is compression right?)
ΔU=nCvΔT



The Attempt at a Solution



Initial pressure = 1.22 * 10^5 pa
Final pressure = 3.66 * 10^ 5 Pa
V = 0.200 m^3

I tried to solve ΔU=5/2*(P2V2-P1V1) but I do not know V1..

Also U=-∫pdV right.. I am messing up, though its pretty simple I guess.
Can anybody help me out please?
 
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  • #2
You need to use the differential form of the equations:

dU=nCvdT=-PdV

You then need to substitute the ideal gas law into the right hand side of this equation, and then figure out how to integrate it. This might all be worked out in your textbook.

Chet
 

FAQ: Ideal diatomic gas undergoing adiabatic compression

1. What is an ideal diatomic gas?

An ideal diatomic gas is a theoretical gas composed of molecules that have two atoms each, such as oxygen (O2) and nitrogen (N2). It follows the laws of ideal gas behavior, which assumes that the gas particles have no volume and do not interact with each other.

2. What does adiabatic compression mean?

Adiabatic compression refers to the process of compressing a gas without any heat exchange with the surroundings. This means that no energy is added or removed from the gas during the compression, and its temperature remains constant.

3. How does an ideal diatomic gas behave during adiabatic compression?

An ideal diatomic gas undergoing adiabatic compression follows the adiabatic process, where the pressure and volume of the gas change while its temperature remains constant. This is described by the adiabatic equation, which states that the product of pressure and volume raised to a constant power is equal to a constant value.

4. What happens to the temperature of an ideal diatomic gas during adiabatic compression?

Since no heat is exchanged during adiabatic compression, the temperature of an ideal diatomic gas remains constant. This means that as the gas is compressed, its pressure and volume change, but its temperature remains the same.

5. What is the significance of adiabatic compression for ideal diatomic gases?

Adiabatic compression is an important concept in thermodynamics and is used to describe the behavior of ideal gases in various processes. It helps to understand the relationship between pressure, volume, and temperature of an ideal diatomic gas, and how it changes when no heat is exchanged with the surroundings.

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