Effect of Piston Weight on Pressure in a Cylinder
The piston of a vertical piston-cylinder device containing a gas has a mass of 60 kg and a cross-sectional area of 0.04 m^2, as shown in Fig. 1-58. The local atmospheric pressure is 0.97 bar, and the gravitational acceleration is 9.81 m/s^2, (a) Determine the pressure inside the cylinder. (b) If some heat is transferred to the gas and its volume is doubled, do you expect the pressure inside the cylinder to change?
A gas is contained in a vertical cylinder with a heavy piston. The pressure inside the cylinder and the effect of volume change on pressure are to be determined.
Assumptions Friction between the piston and the cylinder is negligible.
Analysis (a) The gas pressure in the piston-cylinder device depends on the atmospheric pressure and the weight of the piston. Drawing the free-body diagram of the piston as shown in Fig. 1-58 and balancing the vertical forces yield
P A=P_{\mathrm{atm}} A+WSolving for P and substituting,
\begin{aligned}P &=P_{\text {atm }}+\frac{m g}{A} \\&=0.97 \mathrm{bar}+\frac{(60 \mathrm{~kg})\left(9.81 \mathrm{~m} / \mathrm{s}^{2}\right)}{\left(0.04 \mathrm{~m}^{2}\right)}\left(\frac{1 \mathrm{~N}}{1 \mathrm{~kg} \cdot \mathrm{m} / \mathrm{s}^{2}}\right)\left(\frac{1 \mathrm{bar}}{10^{5} \mathrm{~N} / \mathrm{m}^{2}}\right) \\&=1.12 \text { bar }\end{aligned}
(b) The volume change will have no effect on the free-body diagram drawn in part (a), and therefore the pressure inside the cylinder will remain the same.
Discussion If the gas behaves as an ideal gas, the absolute temperature doubles when the volume is doubled at constant pressure.