PLease help me solve this problem with detail works. I will rate and give you po

Question

PLease help me solve this problem with detail works. I will rate and give you points

Water in a piston-cylinder system expands from an initial volume of 0.01 m3 to a final volume of 0.03 m3 (sketched below). The expansion is counteracted by a spring (initially compressed by some amount), with a spring coefficient of 800 kN/m (assume the spring to be linear such that F = kx where F is the force and .r is the displaced distance), which is attached to the 30 cm diameter piston. The initial quality and pressure of the water in the cylinder is known to be 0.4 and 2.5 MPa, respectively. Assume an atmospheric pressure of 100 kPa acting on the top of the piston. Determine the work done by the system as the steam expands and the magnitude and direction of the heat transfer that has occurred during this process.

Explanation / Answer

Total pressure acting, P= 105 +8*105x/Area Pa.

Work done=?PdV=?0.010.03 (105+8*105x/A)*Adx

=105?0.010.03(0.0706+8x)dx

=461.37 J

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