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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.

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

A sealed cylindrical container, equipped with a frictionless piston and a spring at the top, holds a specific quantity of air. The container's initial conditions have the spring just making contact with the piston, indicating the beginning of compression or expansion. After heating, the piston ascends by 50 mm. Calculate the final temperature and work done by the expanding air.

Solve a thermodynamics problem involving a sealed cylindrical container with a frictionless piston and spring. Calculate the final temperature and work done by expanding air using the Ideal Gas Law and the Work-Energy Principle. This problem involves key concepts from thermodynamics and physics, suitable for university-level students.

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