What is the final pressure of an adiabatically compressed gas in a container?

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SUMMARY

The final pressure of an adiabatically compressed gas in a container can be determined using the adiabatic process equations. Given 2.0 L of air at an initial pressure of 1.0 atm and an initial temperature of -50°C, the gas is compressed to a final volume of 0.5 L. The final pressure can be calculated using the relation P2 = P1 * (V1/V2)^(γ), where γ (gamma) for air is approximately 1.4. Thus, the final pressure is significantly higher than the initial pressure due to the reduction in volume.

PREREQUISITES
  • Understanding of the Ideal Gas Law
  • Knowledge of adiabatic processes in thermodynamics
  • Familiarity with the concept of specific heat ratios (γ)
  • Basic algebra for manipulating equations
NEXT STEPS
  • Study the derivation of the adiabatic process equations
  • Learn about the Ideal Gas Law and its applications
  • Explore the concept of specific heat capacities for different gases
  • Investigate real-world applications of adiabatic compression in engineering
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Students in thermodynamics, engineers working with gas systems, and anyone interested in understanding the behavior of gases under compression.

de3tz
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Homework Statement


a container with air (M = 29 g/mol, treated as an ideal gas). In the container, we have 2.0 L of the gas with p1 = 1.0 atm at T1 = – 50C. The gas is compressed adiabatically to a final volume of 0.5 L. What is its final pressure?


Homework Equations


I am really not sure, as the moles are not given, and the only equation I have encountered for this problem involves moles.


The Attempt at a Solution


I attempted using ideal gas law, but since the process is adiabatic, the answer does not apply. I am truly confused.
 
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Do you think you could find moles? I mean, you have Pressure, Volume, and Temperature.
 

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