A certain amount of gas of volume V at $27 ° C$ temperature and pressure $2 * 1 0^{7} N m^{- 2}$ expands isothermally until its volume gets doubled. Late it expands adiabatically until its volume gets redoubled. The final pressure of the gas will be

(Use $γ$ = 1.5):

Option 1 - 3.536 × 105 Pa

Option 2 - 3.536 × 106 Pa

Option 3 - 1.25×106 Pa

Option 4 - 1.25 × 105 Pa

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Vishal Baghel | Contributor-Level 10

7 months ago

Correct Option - 2

Detailed Solution:

$P_{1} = 2 * 1 0^{7} P a$

$P_{1} v_{1} = P_{2} v_{2}$

Since v₂ = 2v₁ Hence $P_{2} = \frac{P_{1}}{2} (I s o t h e r m a l E x p a n s i o n)$

$P_{2} = 1 * 1 0^{7} P a$

$P_{2} {(v_{2})}^{y} = P_{3} {(2 v_{2})}^{y}$

$P_{3} = \frac{1 * 1 0^{7}}{2^{1.5}} = 3.536 * 1 0^{6} P a$

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A certain amount of gas of volume V at 2 7 ° C temperature and pressure 2 * 1 0 7 N m − 2 expands isothermally until its volume gets doubled. Late it expands adiabatically until its volume gets redoubled. The final pressure of the gas will be (Use γ = 1.5):

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