A certain amount of gas of volume \(V\) at \(27^{o}\,C\) temperature and pressure \(2 \times 10^{7} \;Nm ^{-2}\) 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 \(\gamma=1.5\) )

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Answer & Solution

Correct Answer

(B) \(3.536 \times 10^{6}\,Pa\)

Step-by-step Solution

Detailed explanation

\(P _{1}=2 \times 10^{7} Pa\)

\(P _{1} V _{1}= P _{2} V _{2}\)

Since \(V_{2}=2 V_{1}\) Hence \(P_{2}=P_{1} / 2\) (isothermal expansion)

\(P _{2}=1 \times 10^{7} Pa\)

\(P _{2}\left( V _{2}\right)^{\gamma}= P _{3}\left(2 V _{2}\right)^{\gamma}\)

\(P _{3}=\frac{1 \times 10^{7}}{2^{1.5}}=3.536 \times 10^{6}\)

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