Question

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.

Answer 1

I = 12.706 Amps

Step-by-step 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.