Question

A cylinder with an inside diameter of 105mm is 2.75 meters long. It contains a gas at 790torr. If a piston compresses the gas by 1.2m, what is now the pressure of the gas inside the cylinder in psi?

Answer 1

Answer on Question #48028-Physics – Mechanics | Kinematics | Dynamics

A cylinder with an inside diameter of $d = 105 \, \text{mm} = 0.105 \, \text{m}$ is $h_1 = 2.75$ meters long. It contains a gas at $p_1 = 790 \, \text{torr}$. If a piston compresses the gas by $\Delta h = 1.2 \, \text{m}$, what is now the pressure of the gas inside the cylinder in psi?

Solution

From the Boyle's law:

$$p_1 V_1 = p_2 V_2 \rightarrow p_2 = p_1 \frac{V_1}{V_2},$$

where $V_1 = \pi d^2 h_1$ and $V_2 = \pi d^2 (h_1 - \Delta h)$.

New pressure of the gas inside the cylinder is

$$p_2 = p_1 \frac{\pi d^2 h_1}{\pi d^2 (h_1 - \Delta h)} = p_1 \frac{h_1}{(h_1 - \Delta h)} = 790 \, \text{torr} \cdot 1.93 \cdot 10^{-2} \frac{\text{psi}}{\text{torr}} \frac{2.75 \, \text{m}}{(2.75 \, \text{m} - 1.2 \, \text{m})} = 27.05 \, \text{psi}.$$

Answer: 27.05 psi.

https://www.AssignmentExpert.com