This problem involves a piston-cylinder device with a set of stops, initially containing steam, and involves determining the compression work and final temperatures after cooling. Here's the breakdown:

Given dataThis problem involves a piston-cylinder device with a set of stops, initially containing steam, and involves determining the compression work and final temperatures after cooling. Here's the breakdown:

Given

• Initial state:

  • $P_1 = 1.0 \, \text{MPa}$
  • $T_1 = 400^\circ C$
  • Mass of steam: $m = 0.3 \, \text{kg}$
  • Stops correspond to 60% of the initial volume.

• Final state:

  • Part (a): $P_2 = 1.0 \, \text{MPa}$, $T_2 = 250^\circ C$
  • Part (b): $P_2 = 500 \, \text{kPa}$

Steps to Solve:

Step 1: Find properties at the initial state

Using steam tables, we find properties of steam at $P_1 = 1.0 \, \text{MPa}$ and $T_1 = 400^\circ C$:

• From the steam tables, for superheated steam at 1 MPa and 400°C:
  • Specific volume $v_1$
  • Internal energy $u_1$

Now, we can calculate the initial volume: $V_1 = m \cdot v_1$

Step 2: Determine properties at intermediate state (stops)

The stops limit the volume to 60% of the initial volume: $V_{\text{stops}} = 0.6 \cdot V_1$

Step 3: Analyze Part (a) — Final state at $P_2 = 1.0 \, \text{MPa}, T_2 = 250^\circ C$

At this final state, we use steam tables again for $P_2 = 1.0 \, \text{MPa}$ and $T_2 = 250^\circ C$ to find:

• Specific volume $v_2$
• Internal energy $u_2$

Next, we compute the work done using: $W = P_2 \cdot (V_{\text{stops}} - V_2)$

Step 4: Analyze Part (b) — Final state at $P_2 = 500 \, \text{kPa}$

Now, at the final state with $P_2 = 500 \, \text{kPa}$, we calculate:

• Use steam tables for specific volume $v_3$ and temperature at this pressure. Since the volume is limited by the stops, we use the volume at stops to compute the final temperature and properties.

Step 5: Calculate Compression Work for Both Cases

The compression work is calculated from: $W = P \cdot \Delta V$ where $\Delta V$ is the change in volume as the piston moves to the final state.

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