A piston-cylinder device contains 0.05 m3 of water at 200kPa and 25ºC

[b1977]

1. Homework Statement A piston-cylinder device contains 0.05 m3 of water at 200kPa and 25ºC. The cross sectional area of the piston is 0.25 m2. Heat is now transferred to the water, causing part of it to evaporate and expand. When the volume reaches 0.2 m3 the piston reaches a linear spring whose spring constant is 150kN/m. More heat is transferred to the water until the piston rises 30 cm more. Determine:
(i) The final pressure and temperature and
(ii) The work done during this process. Also, show the process on a P-V diagram.

Homework Equations

PV=MRT

The Attempt at a Solution

55 KJ

 

[Redbelly98]

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The Attempt at a Solution

55 KJ

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[Mene]

of work is done on the water.

(i) Using the ideal gas law, we can find the final pressure and temperature of the water. As the volume increases from 0.05 m3 to 0.2 m3, the pressure decreases from 200kPa to 50kPa, assuming constant temperature. Therefore, the final pressure is 50kPa. To find the final temperature, we can use the relationship PV=MRT and solve for T. Using the initial and final conditions, we get T=500 K. Therefore, the final pressure and temperature are 50kPa and 500K, respectively.

(ii) The work done on the water can be calculated by finding the area under the curve on a P-V diagram. Since the process is not isothermal, we cannot use the simple formula W=nRTln(V2/V1). Instead, we can divide the process into two parts: isobaric and isochoric. For the isobaric part, the work done is given by W=PΔV where P is the constant pressure of 200kPa and ΔV is the change in volume from 0.05 m3 to 0.2 m3. This gives us W=30 kJ. For the isochoric part, no work is done since the volume remains constant at 0.2 m3. Therefore, the total work done is 30 kJ.

The process can be shown on a P-V diagram by plotting the initial and final points (0.05 m3, 200kPa) and (0.2 m3, 50kPa) and connecting them with a curved line. The area under this curve represents the work done on the water. At 0.2 m3, the piston reaches a spring with a spring constant of 150kN/m. This causes the pressure to increase rapidly, leading to a steep increase on the P-V diagram. The piston then continues to rise, increasing the volume and pressure until it reaches the final point of 0.5 m3 and 50kPa. This process can be represented by a curved line connecting the points (0.2 m3, 50kPa) and (0.5 m3, 50kPa). The total process can be shown as a curved line connecting the points (0.05 m3, 200kPa) and (0.5 m3,