Questions: A piston-cylinder device initially contains 0.2 kg of steam at 200 kPa and 300 degrees C. Now, the steam is cooled at constant pressure until it is at 150 degrees C. Determine the volume change (in m^3) of the cylinder during this process.

Solution Steps

First, we need to find the specific volume of the steam at the initial state (200 kPa and \(300^{\circ} \mathrm{C}\)). We can use steam tables for this purpose.

From the steam tables:

• At \(200 \, \text{kPa}\) and \(300^{\circ} \mathrm{C}\), the specific volume \(v_1\) is approximately \(0.1272 \, \text{m}^3/\text{kg}\).

Next, we need to find the specific volume of the steam at the final state (200 kPa and \(150^{\circ} \mathrm{C}\)).

From the steam tables:

• At \(200 \, \text{kPa}\) and \(150^{\circ} \mathrm{C}\), the specific volume \(v_2\) is approximately \(0.8857 \, \text{m}^3/\text{kg}\).

Now, we calculate the initial and final volumes using the specific volumes and the mass of the steam.

Initial volume \(V_1\): \[ V_1 = m \cdot v_1 = 0.2 \, \text{kg} \times 0.1272 \, \text{m}^3/\text{kg} = 0.02544 \, \text{m}^3 \]

Final volume \(V_2\): \[ V_2 = m \cdot v_2 = 0.2 \, \text{kg} \times 0.8857 \, \text{m}^3/\text{kg} = 0.1771 \, \text{m}^3 \]

Finally, we determine the volume change \(\Delta V\) by subtracting the initial volume from the final volume.

\[ \Delta V = V_2 - V_1 = 0.1771 \, \text{m}^3 - 0.02544 \, \text{m}^3 = 0.1517 \, \text{m}^3 \]

Final Answer