Two cylinders A and B of equal capacity are connected to each other via a stopcock. A contains a gas at standard temperature and pressure. B is completely evacuated. The entire system is thermally insulated. The stopcock is suddenly opened. Answer the following:

What is the final pressure of the gas in A and B?

#### Solution 1

0.5 atm

The volume available to the gas is doubled as soon as the stopcock between cylinders A and B is opened. Since volume is inversely proportional to pressure, the pressure will decrease to one-half of the original value. Since the initial pressure of the gas is 1 atm, the pressure in each cylinder will be 0.5 atm.

#### Solution 2

Since the final temperature and initial temperature remain the same,

`therefore "P"_2"V"_2 = "P"_1"V"_1`

But P_{1} = 1 atm, v_{1} = V, V_{2} = 2V and P_{2} = ?

`therefore "P"_2 = ("P"_1"V"_1)/"V"_2 = (1xx"V")/"2V"`

= 0.5 atm