A closed gas cylinder is divided into two parts by a piston held tight. The pressure and the volume of gas in two parts respectively are ( p , 5 V ) and ( 10 p , V ) . If now the piston is left free and the system undergoes the isothermal process, then the volume of the gas in two parts, respectively are

Question

A closed gas cylinder is divided into two parts by a piston held tight. The pressure and the volume of gas in two parts respectively are ( p , 5 V ) and ( 10 p , V ) . If now the piston is left free and the system undergoes the isothermal process, then the volume of the gas in two parts, respectively are, 4 V , 2 V, 5 V , V, 2 V , 4 V, 3 V , 3 V

MARKS App · Accepted Answer

When the piston is allowed to move the gases are kept separated but the pressure has to be equal ( p 1 = p 2 ) and the final volumes are x and 6 V - x . ∵ p 1 = p 2 P ( 5 V ) = n 1 R T ⇒ n 1 = 5 P V R T ∴ n 1 R T x = n 2 R T 6 V - x ⇒ n 1 x = n 2 6 V - x ∵ 10 p V = n 2 R T ⇒ n 2 = 10 P V R T ⇒ 5 P V x R T = 10 P V R T ( 6 V - x ) ⇒ 1 x = 2 6 V - x ∴ x = 2 V and 6 V - x = 4 V

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