Respuesta :
Answer:
The resulting pressure of the air in the cylinder is 4 atmosphere.
Step-by-step 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 [tex]P_1[/tex] and [tex]V_1[/tex] represent the pressure and volume of the gas at an initial state .
[tex]P_2[/tex] and [tex]V_2[/tex] represent the pressure and volume of the gas at an final state .
According to Boyle's Law,
[tex]P_1V_1=P_2V_2[/tex]
Substitute, [tex]P_1=1\ atm,\ V_1=2\ l,\ V_2=0.50\ l[/tex]
[tex]1\times 2=P_2\times 0.50[/tex]
[tex]P_2=\frac{2\ l}{0.50\ l}\times 1\ atm[/tex]
[tex]P_2=4\ atm[/tex]
Therefore, the resulting pressure of the air in the cylinder is 4 atmosphere.
