Question

A vertical cylinder–piston device contains a fixed mass of gas in equilibrium. Cross-sectional area of the piston is \(A = 0.05\ \text{m}^2\). Gas pressure is 150 kPa. Find the mass of the piston (kg). Assume atmospheric pressure = 100 kPa and g = 9.81\ \text{m/s}^2. Round off to 2 decimals.

Hint:

In piston–cylinder systems, net gas pressure above atmospheric supports the piston weight. Use force balance: \((P_{\text{gas}} - P_{\text{atm}})A = mg\).

Answer 1

Correct Answer: 254

Force balance on piston in equilibrium:
\[ P_{\text{gas}} A = P_{\text{atm}} A + mg \] Rearrange for mass:
\[ mg = (P_{\text{gas}} - P_{\text{atm}}) A \] \[ m = \frac{(150000 - 100000)\times 0.05}{9.81} \] Compute:
\[ m = \frac{50000 \times 0.05}{9.81} \] \[ m = \frac{2500}{9.81} = 254.34\ \text{kg} \] Rounded to 2 decimals:
\[ m = 254.34\ \text{kg} \]