prove that adiabatic process obey polytropic law
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Polytropic Compression/Expansion Process. An ideal isothermal process must occur very slowly to keep the gas temperature constant. An ideal adiabatic process must occur very rapidly without any flow of energy in or out of the system.
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A polytropic process is a thermodynamic process that obeys the relation:
{\displaystyle pV^{\,n}=C}
where p is the pressure, V is volume, n is the polytropic index , and C is a constant. The polytropic process equation can describe multiple expansion and compression processes which include heat transfer.
If the ideal gas law applies, a process is polytropic if and only if the ratio (K) of energy transfer as heat to energy transfer as work at each infinitesimal step of the process is kept constant:
{\displaystyle K={\frac {\delta Q}{\delta W}}={\text{constant}}}
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A polytropic process is a thermodynamic process that obeys the relation:
{\displaystyle pV^{\,n}=C}
where p is the pressure, V is volume, n is the polytropic index , and C is a constant. The polytropic process equation can describe multiple expansion and compression processes which include heat transfer.
If the ideal gas law applies, a process is polytropic if and only if the ratio (K) of energy transfer as heat to energy transfer as work at each infinitesimal step of the process is kept constant:
{\displaystyle K={\frac {\delta Q}{\delta W}}={\text{constant}}}
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