A certain amount of gas of volume V at 27 ° C temperature and pressure 2 × 10 7 N   m - 2…

A certain amount of gas of volume V at 27°C temperature and pressure 2×107N m-2 expands isothermally until its volume gets doubled. Later it expands adiabatically until its volume gets redoubled. The final pressure of the gas will be (Use γ=1.5)
  1. 3.536×105 Pa
  2. 3.536×106 Pa
  3. 1.25×106 Pa
  4. 1.25×105 Pa

Solution

Given here, P1=2×107 N m-2=2×107 Pa

Using Boyle's law,

P1V1=P2V2

Since V2=2V1.

Hence, P2=P12 (isothermal expansion)

P2=1×107 Pa

Now, during adiabatic expansion, 

P2V2γ=P32V2γ

P3=1×10721.5=3.536×106 Pa

Asked in: JEE Main 2022 (25 Jul Shift 1)

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