Question

A piston–cylinder device contains 15 kg of saturated refrigerant-134a vapor at 280kPa. A resistance heater inside the cylinder with a value of 110V is used to transfer heat of 20.67kJ/kg to the refrigerant at constant pressure for 6min. Determine the current supplied if the final temperature is 75℃

Answer 1

18.77 A

Step-by-step explanation:

To solve this we use the energy balance equation, that is:

`E_(in)-E_(out)=\Delta E_(sys)\\\\Q_(in)+W_(in)+W_(out)=\Delta U\\\\Q_(in)+W_(in)=\Delta U\\\\But\ W_(in)=Voltage(V)*Current(I)*change\ in\ time(\Delta t)=VI\Delta t,\Delta U=m(h_2-h_1)\\\\Given\ that\ m=15kg,V=110\ V,\Delta t=6\ min = (6*60\ s)=360\ s,Q_(in)=20.67\ kJ/kg*15\ kg=310.05\ kJ=310050\ J\\\\From\ table: At\ P_1=280kPa, h_1=249.71\ kJ/kg=249710\ J/kg;At\ P_2=280kPa \ and\ T_1=75^oC,P_2=319.95\ kJ/kg=319950\ J/kg\\\\Substituting:\\\\310500+(110*360*I)=15(319950-249710)\\\\`

`39600I=1053600-310500\\\\39600I=743100\\\\I=18.77\ A`