Exams › GATE › Technical

Consider a fully adiabatic piston-cylinder arrangement as shown in the figure. The piston is massless and cross-sectional area of the cylinder is A. The fluid inside the cylinder is air (considered as a perfect gas), with γ being the ratio of the specific heat at constant pressure to the specific heat at constant volume for air. The piston is initially located at a position L1. The initial pressure of the air inside the cylinder is P1 >> P0, where P0 is the atmospheric pressure. The stop S1 is instantaneously removed and the piston moves to the position L2, where the equilibrium pressure of air inside the cylinder is P2 >> P0. What is the work done by the piston on the atmosphere during this process?

1. 0
2. P0 A (L2 - L1)
3. P1 A L1 ln(L1/L2)
4. (P2 L2 - P1 L1)A / (1 - γ)

Correct answer: P0 A (L2 - L1)

Solution

The work done by the piston on the atmosphere is determined by the pressure exerted by the atmosphere (P0) and the change in volume as the piston moves from L1 to L2. Since the process is adiabatic and the piston is moving against atmospheric pressure, the work is calculated as the atmospheric pressure multiplied by the cross-sectional area and the distance moved, which is represented by P0 A (L2 - L1).

Related GATE Technical questions

• Assuming constant temperature condition and air to be an ideal gas, the variation in atmospheric pressure with height calculated from fluid statics is
• A hollow cylinder has length L, inner radius r1, outer radius r2, and thermal conductivity k. The thermal resistance of the cylinder for radial conduction is
• Consider the radiation heat exchange inside an annulus between two very long concentric cylinders. The radius of the outer cylinder is Ro and that of the inner cylinder is Ri. The radiation view factor of the outer cylinder onto itself is
• The internal energy of an ideal gas is a function of
• In the phase diagram shown in the figure, four samples of the same composition are heated to temperatures marked by a, b, c and d. At which temperature will a sample get solutionized the fastest?
• The welding process which uses a blanket of fusible granular flux is

⚔️ Practice GATE Technical free + battle 1v1 →