Is the Ideal Gas Law Applicable to Non-Isothermal Processes? | Homework Question

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SUMMARY

The Ideal Gas Law, represented as PV = mRT, is applicable to both isothermal and non-isothermal processes, including polytropic processes. It serves as an equation of state that relates pressure (P), volume (V), and temperature (T) under fixed amounts of gas. During a polytropic process, while the relationship PV^γ = constant holds, temperature (T) will vary as pressure (P) and volume (V) change, ensuring that the Ideal Gas Law remains valid.

PREREQUISITES
  • Understanding of the Ideal Gas Law (PV = mRT)
  • Knowledge of polytropic processes and their equations (PV^γ = constant)
  • Familiarity with thermodynamic principles
  • Basic algebra for manipulating equations
NEXT STEPS
  • Study the derivation and applications of the Ideal Gas Law in various thermodynamic processes
  • Explore the concept of polytropic processes and their significance in thermodynamics
  • Learn about the relationship between pressure, volume, and temperature in non-isothermal conditions
  • Investigate real gas behavior and deviations from the Ideal Gas Law
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Students of thermodynamics, physics enthusiasts, and professionals in engineering fields who require a solid understanding of gas laws and their applications in various processes.

SherlockOhms
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Homework Statement


Is the ideal gas law, PV = mRT, only applicable to processes which are carried out isothermally? I mean, can it not be applied to a polytropic process, PVn = k.

Homework Equations


See above.

The Attempt at a Solution


N.A.
 
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SherlockOhms said:
Is the ideal gas law, PV = mRT, only applicable to processes which are carried out isothermally?
No. It is an equation of state: it relates P, V, and T (assuming n fixed). It is valid everywhere (you can't have an ideal gas at pressure ##P_1## occupying volume ##V_1##, and measure temperature ##T_1##, and have the same amount of an ideal gas also at ##P_1## and ##V_1## and measure ##T_2 \neq T_1##).

For a polytropic process, the equation only tells you what remains constant during the process. In the formulation ##PV^\gamma = \text{const.}##, then ##T## must change when ##P## and ##V## change, such that ##PV = nRT## is maintained.
 
Got it. Thanks for that.
 

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