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Question

A mass of diatomic gas (γ=1.4) at a pressure of 2 atm is compressed adiabatically so that its temperature rise from 27oC to 927oC. The pressure of the gas is final state is
  1. 68.7 atm
  2. 28 atm
  3. 8 atm
  4. 256 atm

A
28 atm
B
256 atm
C
8 atm
D
68.7 atm
Solution
Verified by Toppr

PVγ= constant T1=273+27=300K
P(TP)γ= constant T2=273+927=1200K

P1γTγ= constant
P1γ1Tγ1=P1γ2Tγ2
211.4(300)1.4=P11.42(1200)1.4
(P2P1)1γ=(T1T2)γP2P1=(T1T2)γ1γ

(P1P2)1γ=(T2T1)γ

(P1P2)11.4=(1200300)1.4

(P1P2)0.4=(4)1.4

(P2P1)0.4=41.4

P2=P14(1.4/0.4)=P14(7/2)

=P1(27)=2×128=256

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