Let's break down the problem from the thermodynamics assignment:

Problem Breakdown:

1. System Setup:

   • Cylindrical Container: Equipped with a frictionless piston and a spring.
   • Air Mass: 6 grams of air inside the container.
   • Spring Constant (k): 400 kN/m.
   • Piston: Mass of 300 kg.
   • Cylinder Dimensions: Internal height = 150 mm, diameter = 200 mm.
   • Piston Movement: The piston rises by 50 mm after heating.

2. Tasks:

   • Final Temperature: You need to calculate the final temperature of the air when the piston begins to move.
   • Work Done: Compute the work done by the expanding air against the piston.

Assumptions and Parameters to Use:

• Initial state: Piston is in equilibrium (spring just touching the piston, no initial force).
• Air Expansion: Causes piston to move upwards.

Key Equations:

1. Ideal Gas Law: $PV = nRT$ Where:

   • $P$ is the pressure,
   • $V$ is the volume,
   • $n$ is the number of moles of air,
   • $R$ is the gas constant (8.314 J/mol·K),
   • $T$ is the temperature.

2. Work Done (W): $W = P \Delta V$ Where $\Delta V$ is the change in volume due to the piston movement.

3. Force due to Spring Compression: $F_{\text{spring}} = kx$ Where $x$ is the compression or extension of the spring from its equilibrium position.

4. Volume of the Cylinder: $V = \pi r^2 h$ Where $r$ is the radius of the cylinder, and $h$ is the height of the air column.

Shall I proceed with calculating the temperature and work done based on this data? Feel free to ask for specific details on any step!