Question

Consider a weightless, frictionless piston with a 2 kg mass placed on it as shown in the figure. At equilibrium in position 1, the cylinder contains 0.1 kg of air. The piston cross-sectional area is 0.01 m². The ambient pressure in the surroundings outside the piston-cylinder arrangement is 0 bar (absolute). When the mass above the piston is removed instantaneously, it moves up and hits the stop at position 2, which is 0.1 m above the initial position.
Assuming \( g = 9.81 \, {m/s}^2 \), the thermodynamic work done by the system during this process is ________ J (answer in integer).

Hint:

In a system where there is no external pressure or force acting on the gas, no work is done by the system despite any movement of the piston.

Answer 1

Step 1: Understanding the work done. 
The problem involves a weightless, frictionless piston with a given mass placed on it, which moves up when the mass is removed. The thermodynamic work in this case is done by the system as the air expands and pushes the piston upward. The work done is given by: \[ W = P \Delta V \] where:
\( P \) is the pressure exerted by the gas,
\( \Delta V \) is the change in volume.
Step 2: Pressure inside the cylinder. 
Since the ambient pressure outside the piston-cylinder arrangement is 0 bar (absolute), the pressure inside the cylinder is due to the weight of the piston and the air above it. However, since the problem states that the pressure outside the cylinder is 0 bar (absolute), and there is no external force acting to compress the gas, the pressure inside the cylinder becomes 0. 
Step 3: Work calculation. 
Since the pressure inside the cylinder is 0, the work done during the expansion is: \[ W = P \Delta V = 0 \times \Delta V = 0. \] 
Final Answer: The thermodynamic work done by the system is \( \boxed{0} \, {J} \).