Question

An ideal gas is confined within a closed cylinder at a pressure of 2.026 × 105 Pa by a piston. The piston moves until the volume of the gas is reduced to one-ninth of the initial volume. What is the final pressure of the gas when its temperature returns to its initial value?

Answer 1

The final pressure of the gas when its temperature returns to its initial value
`1.8234* 10^6` Pa.

Explanation:

Given : An ideal gas is confined within a closed cylinder at a pressure of
`2.026* 10^5` Pa by a piston. The piston moves until the volume of the gas is reduced to one-ninth of the initial volume.

To find : What is the final pressure of the gas when its temperature returns to its initial value?

Solution :

Since the temperature is constant .

The relation between P and V is given by,

`P_1* V_1 = P_2* V_2`

`(P_1)/(P_2)=(V_2)/(V_1)` ....(1)

The piston moves until the volume of the gas is reduced to one-ninth of the initial volume i.e.
`V_2=(V_1)/(9)`

or
`(V_2)/(V_1)=(1)/(9)`

`P_1=2.026* 10^5`

Substitute in equation (1),

`(2.026* 10^5)/(P_2)=(1)/(9)`

`P_2=9* 2.026* 10^5`

`P_2=18.234* 10^5`

`P_2=1.8234* 10^6`

The final pressure of the gas when its temperature returns to its initial value
`1.8234* 10^6` Pa.