Following figure shows on adiabatic cylindrical container of volume $${{V}_{0}}$$ divided by an adiabatic smooth piston (area of cross-section = A) in two equal parts. An ideal gas $$({{C}_{P}}/{{C}_{V}}=\gamma )$$ is at pressure P1 and temperature T1 in left part and gas at pressure P2 and temperature T2 in right part. The piston is slowly displaced and released at a position where it can stay in equilibrium. The final pressure of the two parts will be (Suppose x = displacement of the piston)

Question

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$$\frac{{{P}_{2}}{{\left( \frac{{{V}_{0}}}{2} \right)}^{\gamma }}}{{{\left( \frac{{{V}_{0}}}{2}+Ax \right)}^{\gamma }}}$$

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$${{P}_{2}}$$

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$${{P}_{1}}$$

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80 gm

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$$\frac{{{P}_{2}}{{\left( \frac{{{V}_{0}}}{2} \right)}^{\gamma }}}{{{\left( \frac{{{V}_{0}}}{2}+Ax \right)}^{\gamma }}}$$

1.	Following figure shows on adiabatic cylindrical container of volume \[{{V}_{0}}\] divided by an adiabatic smooth piston (area of cross-section = A) in two equal parts. An ideal gas \[({{C}_{P}}/{{C}_{V}}=\gamma )\] is at pressure P1 and temperature T1 in left part and gas at pressure P2 and temperature T2 in right part. The piston is slowly displaced and released at a position where it can stay in equilibrium. The final pressure of the two parts will be (Suppose x = displacement of the piston)
A.	\[{{P}_{2}}\]
B.	\[{{P}_{1}}\]
C.	80 gm
D.	\[\frac{{{P}_{2}}{{\left( \frac{{{V}_{0}}}{2} \right)}^{\gamma }}}{{{\left( \frac{{{V}_{0}}}{2}+Ax \right)}^{\gamma }}}\]
Answer» D. \[\frac{{{P}_{2}}{{\left( \frac{{{V}_{0}}}{2} \right)}^{\gamma }}}{{{\left( \frac{{{V}_{0}}}{2}+Ax \right)}^{\gamma }}}\]

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