A cylinder measuring 7.7 cm wide and 9.3 cm high is filled with gas. The piston is pushed down with a steady force measured to be 17 N. Calculate the pressure of the gas inside the cylinder. Write your answer in units of kilo pascals round your answer to two significant digits.
To calculate the pressure of the gas inside the cylinder, we can use the formula:
Pressure = Force / Area
First, we need to calculate the area of the cylinder's base. The area of a circle is given by the formula:
Area = π * radius^2
Given that the cylinder's width is 7.7 cm, the radius can be calculated as half of the width:
Radius = 7.7 cm / 2 = 3.85 cm
Converting the radius to meters:
Radius = 3.85 cm / 100 = 0.0385 m
Now, we can calculate the area of the base:
Area = π * (0.0385 m)^2
Next, we can calculate the pressure:
Pressure = 17 N / Area
Finally, converting the pressure to kilopascals (1 Pa = 0.001 kPa):
Pressure = Pressure / 1000 kPa
Calculating the pressure and rounding to two significant digits:
Pressure = (17 N) / (π * (0.0385 m)^2) / 1000 kPa
Pressure ≈ 35 kPa
Therefore, the pressure of the gas inside the cylinder is approximately 35 kPa.