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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.

Let me calculate these details step-by-step next to match the given answers.

A piston-cylinder device with a set of stops initially contains 0.3 kg of steam at 1.0 MPa and 400°C. The location of the stops corresponds to 60 percent of the initial volume. Now the steam is cooled. Determine the compression work if the final state is (a) 1.0 MPa and 250°C and (b) 500 kPa. (c) Also determine the temperature at the final state in part (b).

Solve a thermodynamics problem involving a piston-cylinder device. Calculate the compression work when steam is cooled to specific final states and determine the final temperature using the properties of steam from tables. Ideal for undergraduate students studying thermodynamics.

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