How Does Adiabatic Compression Affect Gas Pressure?

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SUMMARY

The discussion focuses on the adiabatic compression of an ideal monatomic gas, initially at a pressure of 1.6 x 104 Pa, which undergoes a volume reduction by half. The key relationship governing this process is defined by the equation P Vγ = constant, where γ (gamma) is the adiabatic index, specifically 3/2 for monatomic gases. Participants express confusion regarding the application of the work equation W = -PΔV, indicating a need for clarity on the relationship between pressure and volume during adiabatic processes.

PREREQUISITES
  • Understanding of ideal gas laws
  • Familiarity with adiabatic processes
  • Knowledge of thermodynamic concepts, particularly specific heat capacities (CP and CV)
  • Basic algebra for manipulating equations
NEXT STEPS
  • Study the derivation of the adiabatic process equation P Vγ = constant
  • Learn about the significance of the adiabatic index (γ) in thermodynamics
  • Explore examples of adiabatic processes in real-world applications
  • Investigate the differences between adiabatic and isothermal processes
USEFUL FOR

This discussion is beneficial for physics students, thermodynamics researchers, and engineers involved in gas dynamics and energy systems, particularly those focusing on the behavior of gases under varying pressure and volume conditions.

ghostbuster25
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a sample of an idel monotomic gas is intially at a pressure 1.6*10^4Pa and undergoes an adiabatic compression which halves the volume. What is the final pressure?

ive been trying to find a way of useing the equation W=-P\DeltaV but am starting to think this is the wrong one as i can't see how i can use it.

any suggestions?
 
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Find the relation between pressure and volume of an ideal gas during an adiabatic process.

ehild
 
sorry i can't see it :(,

i can only see that p*V= a constant but not sure how to use that here!

am i way off track?
 
im still unclear on the relationship after reading that
 
The mathematical equation for an ideal fluid undergoing a reversible (i.e., no entropy generation) adiabatic process is

P V^{\gamma} = \operatorname{constant} \qquad

where P is pressure, V is volume, and

\gamma = {C_{P} \over C_{V}} = \frac{\alpha + 1}{\alpha},

CP being the specific heat for constant pressure, CV being the specific heat for constant volume, γ is the adiabatic index, and α is the number of degrees of freedom divided by 2 (3/2 for monatomic gas, 5/2 for diatomic gas).

ehild
 

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