I have a free floating piston cylinder device that contains 1 kg of a 25% qualit

Question

I have a free floating piston cylinder device that contains 1 kg of a 25% quality saturated mixture of water at 150C. A resistance heater with a power rating of 1800 Watts operates for a time causing all of the liquid to become vapor. The piston is then locked into place and water is heated until it reaches 200C. Determine the initial and final pressure, the total energy of electrical work added to the water, the total boundary work done and the total time for the process. Since it is a piston cylinder device the pressure is constant. However after that I am totally lost on this problem. Some help would be greatly appreciated. Thank you

Explanation / Answer

the amount of water that gets evaporated = .25*1kg=250gms

that is = 250/18 molesof H20

so we see that the power used for 250/18 moles of H20 is 1800 so for 1 mole = 1800*18/250 =129.6 W

for the initial and the final pressure

we see that the volume occupied remains same as the system remains same and just there is a transformation of state from liquid to gaseous

as the volume remains same as as well as the moles the final and the initial pressure are directly proportional to the the temperatures

so P1/P2 =[273+150]/[273+200]

this gives us the pressure relationship

now the total energy of the electrical work added to water = moles *R*change in temp

-=250*R*[200-150]/18

the total time taken is =work done /power

= 250*R*[200-150]/1800*18 s

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