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

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 = $\frac{diameter}{2}$

              = $\frac{2.6 cm}{2}$

              = 1.3 cm

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

As, area of cylinder = $\pi \times r^{2}$

                                = $3.414 \times (0.013 m)^{2}$

                                = $5.77 \times 10^{-4} m^{2}$

Relation between pressure and force is as follows.

             Pressure = $\frac{Force}{Area}$

                         = $\frac{15 N}{5.77 \times 10^{-4} m^{2}}$

                         = 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.