A mass of 12 kg saturated refrigerant-134a vapor is contained in a piston-cylinder device at 240 kPa. Now 300 kJ of heat is transferred to the refrigerant at constant pressure while 110-V source supplies current to a resistor within the cylinder for 6 min. Determine the current supplied if the final temperature is 70 degrees C. Also, show the process on a T-v diagram with respect to the saturation lines.

I = 12.706 Amps

Explanation:

Given:

- The mass of saturated R-134a m = 12 kg

- The initial Conditions

      P_1 = 240 KPa

      Saturated Vapor

- The final Conditions

      P_2 = 240 KPa

      T_2 = 70° C

- The amount of Heat transferred Q_in = 300 KJ

- The voltage of current source V = 110 V

- The current supplied by the source = I

- The time duration Δt = 6 min

Find:

Determine the current supplied I.

Solution:

- Look-up enthalpies h_1 and h_2 at both states using Tables A-11 and A-13.

       P_1 = 240 KPa    

       Saturated Vapor > h_1 = h_g = 247.32 KJ/kg

       P_2 = 240 KPa

       T_2 = 70° C        > h_2 = 314.53 KJ/kg

- Using First Thermodynamic Law, set up an energy balance:

                           E_in - E_out = ΔE_system

                           Q_in + W_electric,in - W_out = Δ U

                           Q_in + V*I*Δt - W_out = Δ U

                           Q_in + V*I*Δt = Δ H

                           Q_in + V*I*Δt = m*( h_2 - h_1 )

- Make the current I the subject of the expression above:

                            V*I*Δt = m*( h_2 - h_1 ) - Q_in

                            I = [ m*( h_2 - h_1 ) - Q_in ] / V*Δt

- Plug in the values in the expression derived above and evaluate current of source I:

                            I = [ 12*( 314.53 - 247.32 ) - 300 ]*1000 / 110*6*60

                            I = 12.706 Amps                              

- The required source of current is I = 12.706 Amps.

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