Question

If a tire pump whose cylinder has a volume of 2.0 liters at 1 atmosphere of pressure

compresses the air to a volume of 0.50 liters without releasing any of the air, what is

the resulting pressure of the air in the cylinder?

Answer 1

The resulting pressure of the air in the cylinder is 4 atmosphere.

Explanation:

Given : If a tire pump whose cylinder has a volume of 2.0 liters at 1 atmosphere of pressure compresses the air to a volume of 0.50 liters without releasing any of the air.

To find : What is the resulting pressure of the air in the cylinder?

Solution :

Let
`P_1` and
`V_1` represent the pressure and volume of the gas at an initial state .

`P_2` and
`V_2` represent the pressure and volume of the gas at an final state .

According to Boyle's Law,

`P_1V_1=P_2V_2`

Substitute,
`P_1=1\ atm,\ V_1=2\ l,\ V_2=0.50\ l`

`1* 2=P_2* 0.50`

`P_2=(2\ l)/(0.50\ l)* 1\ atm`

`P_2=4\ atm`

Therefore, the resulting pressure of the air in the cylinder is 4 atmosphere.