Question

A cylinder measuring wide and high is filled with gas. The piston is pushed down with a steady force measured to be . Calculate the pressure of the gas inside the cylinder. Write your answer in units of kilopascals. Be sure your answer has the correct number of significant digits

Answer 1

The pressure of the gas inside the cylinder is 0.375 kPa.

Step-by-step explanation:

To calculate the pressure of the gas inside the cylinder, we can use the formula:

Pressure = Force / Area

Given that the force exerted by the piston is measured to be 150 Pa and the area of the piston is 0.40 m², we can substitute these values into the formula:

Pressure = 150 Pa / 0.40 m²

Calculating this, we find that the pressure of the gas inside the cylinder is 375 Pa.

Since the question asks for the answer in units of kilopascals, we can convert 375 Pa to kilopascals by dividing by 1000.

Therefore, the pressure of the gas inside the cylinder is 0.375 kPa.

Answer 2

Step-by-step explanation:

Let us assume that the given cylinder is 2.6 cm wide and its height is 3.1 cm. And, when piston is pushed down then the steady force is equal to 15 N.

Now, radius of the cylinder will be as follows.

r =
`(diameter)/(2)`

=
`(2.6 cm)/(2)`

= 1.3 cm

or, = 0.013 m (as 1 m = 100 cm)

As, area of cylinder =
`\pi * r^(2)`

=
`3.414 * (0.013 m)^(2)`

=
`5.77 * 10^(-4) m^(2)`

Relation between pressure and force is as follows.

Pressure =
`(Force)/(Area)`

=
`(15 N)/(5.77 * 10^(-4) m^(2))`

= 25996
`N/m^(2)`

Since, 1
`N/m^(2)` = 1 Pa (as 1 kPa = 1000 Pa)

Therefore, P = 25996
`N/m^(2)`

= 25.99 kPa

= 26 kPa (approx)

Thus, we can conclude that pressure of the gas inside the cylinder is 26 kPa.