Ideal diatomic gas undergoing adiabatic compression

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SUMMARY

An ideal diatomic gas undergoing adiabatic compression experiences a change in internal energy defined by the equation ΔU=nCvΔT, where Cv is the specific heat capacity at constant volume. Given the initial pressure of 1.20 atm (1.22 x 10^5 Pa) and a final pressure of 3.60 atm (3.66 x 10^5 Pa), the work done by the gas can be calculated using the relationship ΔU=W since Q=0 in adiabatic processes. The integration of the differential form dU=nCvdT=-PdV is essential for deriving the work done during the compression.

PREREQUISITES
  • Understanding of ideal gas laws and equations
  • Knowledge of thermodynamic principles, specifically adiabatic processes
  • Familiarity with the concept of internal energy and specific heat capacities
  • Ability to perform integration in the context of physics equations
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  • Study the derivation of the adiabatic process equations in thermodynamics
  • Learn about the ideal gas law and its applications in different thermodynamic processes
  • Explore the integration techniques for thermodynamic equations, particularly for work done
  • Review the specific heat capacities for diatomic gases and their implications in energy calculations
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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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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
 

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