Refrigeration Process: Freon 13 Heat Exchanger -25C, 1MPa

[thermoA]

Homework Statement

Freon 13 is used as the refrigent in a commerical refrigeration process. At one point Freon 13 enters a heat exchanger at a pressure of 1 MPa and -25 degrees C. The liquid absorbs 115 KJ of heat per kg of Freon 13 entering the heat exchanger and exits at the same temp and pressure, but with a quality of 96%.

Specifice volume of saturated liquid Freon 13 at 1 MPa and -25 degrees C is 5% of the saturated capor volume at this pressure and temperature.
Also, vapor phase as these conditions is not an ideal gas.
Critical Temp is 302 K and critical pressure is 4 MPa. MW = 104.3 gm/mole.

Homework Equations

What is the enthalpy of vaporization process?
And if the operation temperature of Freon 13 in heat exchanger is lowered to -30 degrees C, what pressure would be required to stay on the saturation curve for vapor liquid equilibrium to carry out the evaporation at this new temperature?

 

[Valkarie]

The Attempt at a Solution I am not sure how to go about solving this problem. I know I must use the given values and equations, but I am not sure which equations I should use.

 

[Mene]

The enthalpy of vaporization process can be calculated using the thermodynamic equation:

ΔHvap = Q/m

Where ΔHvap is the enthalpy of vaporization, Q is the heat absorbed per kg of Freon 13, and m is the mass of Freon 13. Plugging in the given values, we get:

ΔHvap = 115 kJ/kg

To determine the required pressure for the evaporation process at -30 degrees C, we can use the Clausius-Clapeyron equation:

ln(P2/P1) = ΔHvap/R * (1/T1 - 1/T2)

Where P1 and T1 are the initial pressure and temperature, and P2 and T2 are the new pressure and temperature. Rearranging the equation, we get:

P2 = P1 * e^(ΔHvap/R * (1/T1 - 1/T2))

Plugging in the given values, we get:

P2 = 1 MPa * e^(115 kJ/kg / (104.3 gm/mol * 8.314 J/mol*K) * (1/248 K - 1/243 K))

P2 = 1.034 MPa

Therefore, the pressure required for the evaporation process at -30 degrees C is approximately 1.034 MPa. This is slightly higher than the initial pressure of 1 MPa, indicating that a slight increase in pressure is needed to maintain the saturation curve for vapor-liquid equilibrium at the lower temperature.