Question

A closed gas cylinder is divided into two parts by a piston
held tight. The pressure and volume of gas in two parts
respectively are (P, 5V) and (10P, V). If now the piston is left
free and the system undergoes isothermal process, then
the volumes of the gas in two parts respectively are
(a) 2V, 4V (b) 3V, 3V
(c) 5V, V (d)10/11 V, 20/11 V

Answer 1

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 6V - x.

∵p

1

=p

2

P(5V)=n

1

RT

⇒n

1

=

RT

5PV

∴

x

n

1

RT

=

6V−x

n

2

RT

⇒

x

n

1

=

6V−x

n

2

∵10pV=n

2

RT

⇒n

2

=

RT

10PV

⇒

xRT

5PV

=

RT(6V−x)

10PV

⇒

2

1

=

6V−x

2

∴x=2V and 6V−x=4V