An ideal monatomic gas with pressure P , volume V and temperature T is expanded isothermally to a volume 2 V and a final pressure P i . If the same gas is expanded adiabatically to a volume 2 V , th

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An ideal monatomic gas with pressure P , volume V and temperature T is expanded isothermally to a volume 2 V and a final pressure P i ​ . If the same gas is expanded adiabatically to a volume 2 V , the final pressure is P a ​ . The ratio P i ​ P a ​ ​ is

TestHub · Accepted Answer

For isothermal process : ​ P V = P i ​ 2 V P = 2 P i ​ ​ For adiabatic process PV γ = P a ​ ( 2 V ) γ ( ∵ for monatomic gas γ = 5/3 ) [From (i) ] or, 2 P i ​ V 3 5 ​ = P a ​ ( 2 V ) 3 5 ​ ​ ⇒ P i ​ P a ​ ​ = 2 3 5 ​ 2 ​ ⇒ P i ​ P a ​ ​ = 2 3 − 2 ​ ​

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