R-134a is contained in a vertical cylinder fitted with a frictionless piston and

Question

R-134a is contained in a vertical cylinder fitted with a frictionless piston and a set of stops and the volume is 0.05m^3 when the piston is against the upper stops.  The pressure of R-134a must be 200kPa to support the piston when it is not pushed against the stops.  Initially the R-134a is at 200kPa, 40% quality and occupies a volume of 0.03m^3.  The R-134a is then heated to a final temperature of 30 degrees centigrade.

Find the final quality (if saturated) or pressure (if superheated) of the R-134a and its final specific internal energy, u. (ans:  superheated at 346kPa and u=253.13 kJ/kg

Explanation / Answer

Assuming v = 0.0673313 (calculated from previous part of question, not given here)

At T=30 degrees C, Psat = 770.64 kPa. P < Psat, therefore Superheated Vapor.

Per table A-13 (Thermodynamics, Cengel)

At T=30 degress C, va = 0.07231 m^3/kg, Ua = 253.50 kJ/kg, for Pa = 0.32 MPa.

At T=30 degress C, vb = 0.056796 m^3/kg, Ub = 252.36 kJ/kg, for Pa = 0.40 MPa.

vb = 0.056796 < v = 0.0673313 < va = 0.07231

alpha = (v - va) / (vb - va) = (0.0673313 - 0.07231) / ( 0.056796 - 0.07231) = 0.3209166

P = Pa + alpha(Pb - Pa) = 0.32 + 0.3209166*(0.40 - 0.32) = 0.34567 MPa or 345.67 kPa

u = ua + alpha(ub - ua) = 253.50 + 0.3209166*(252.36-253.50) = 253.134 kJ/kg

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