Question

A piston-cylinder device fitted with stops in the cylinder walls contains 2.1 kg of water initially at 150 kPa and 30 °C. Heat is transferred to the system until the final temperature reaches 250 °C. The stops restrict the maximum cylinder volume to be 2200 L. Does the piston hit the stops? Plot the process on a P-v phase diagram and determine the final volume, the final pressure, the work done by the water, and the amount of heat transferred throughout the process.

Answer 1

The piston hits the stops.

P-v plot in the attachment.

Vf = 1.601 L

Pf = 150 kPa

W = 316,60 kJ

Q = 5.977,02 kJ

Step-by-step explanation:

This system is a constant pressure one because the internal pressure always is in equilibrium with the pressure that is generated by the piston weight.

According to this, the final and initial pressure are the same. Considering that the known temperature and pressure values at both of the states the thermodynamic tables can be used to estimate the specific volumes. In this case, I took the values from the book, Fundamentals of Engineering Thermodynamics of Moran and Shapiro. The estimated values are:

`P_(i) = 150 kPa\\T_(i) = 30 C\\v_(i) = 0,001004 m^(3)/kg\\\\\\P_(f) = 150 kPa\\T_(f) = 250 C\\v_(f) = 1,6010 m^(3)/kg\\`

The final volume is calculated as follows (considering that the mass is constant, because is a closed system where there isn´t mass transfer):

`V_(f) =v_(f)*m_(f)=(1,6010)m^(3)/kg*(2,1)kg=3,3621m^(3)=3.362,1 L`

According to the previous calculation, the final volume is higher than the maximum one.

The work that was done by the fluid can be calculated as follows:

`W=m*P*(v_(f)-v_(i))=(2,1)kg*(150)kN/m^(2)*(1,6010-0,001004)m^(3)/kg=316,60kJ`

The heat can be calculated as follows:

`Q=m(h_(f)-h_(i))=(2,1)kg*(2972-125,8)kJ/kg=5.977,02kJ`

The enthalpy values (h), that were included in the previous expression, were also estimated from the book, Fundamentals of Engineering Thermodynamics of Moran and Shapiro.