Question

You pump 25.0 liters of air at atmospheric pressure (101.3 kPa) into a soccer ball that has the volume of 4.50 liters. What is the pressure inside the soccer ball if the temperature does not change?

Answer 1

562.8 kPa

Step-by-step explanation:

We can solve the problem by using Boyle's law, which states that the product between the pressure of a gas kept at constant temperature and its volume is constant:

`p V = const.`

which can also be written as

`p_1 V_1 = p_2 V_2`

In this problem:

`p_1 = 101.3 kPa` is the initial pressure of the gas

`V_1 = 25.0 L` is the initial volume

Later, the gas is pumped into a volume of

`V_2 = 4.5 L`

So we can use the equation above to find
`p_2`, the final pressure of the gas when it is inside the ball:

`p_2 = (p_1 V_1)/(V_2)=((101.3)(25.0))/(4.5)=562.8 kPa`