A Carnot Refrigeration Cycle Operating in the Saturation Dome A Carnot refrigeration cycle is executed in a closed system in the saturated liquid-vapor mixture region using 0.8 kg of refrigerant-134a as the working fluid (Fig. 6-52). The maximum and the minimum temperatures in the cycle are 20

Question

A Carnot Refrigeration Cycle Operating in the Saturation Dome

A Carnot refrigeration cycle is executed in a closed system in the saturated liquid-vapor mixture region using 0.8 kg of refrigerant-134a as the working fluid (Fig. 6-52). The maximum and the minimum temperatures in the cycle are 20 and -8°C , respectively. It is known that the refrigerant is saturated liquid at the end of the heat rejection process, and the net work input to the cycle is 15 k j. Determine the fraction of the mass of the refrigerant that vaporizes during the heat addition process, and the pressure at the end of the heat rejection process.

Accepted Answer

A Carnot refrigeration cycle is executed in a closed system. The mass fraction of the refrigerant that vaporizes during the heat addition process and the pressure at the end of the heat rejection process are to be determined.

Assumptions The refrigerator operates on the ideal Carnot cycle.

Analysis Knowing the high and low temperatures, the coefficient of performance of the cycle is

[latex]\mathrm{COP}_{\mathrm{R}}=\frac{1}{T_{H} / T_{L}-1}=\frac{1}{(20+273 \mathrm{~K}) /(-8+273 \mathrm{~K})-1}=9.464[/latex]

The amount of cooling is determined from the definition of the coefficient of performance to be

[latex]Q_{L}=\operatorname{COP}_{\mathrm{R}} imes W_{ ext {in }}=(9.464)(15 \mathrm{~kJ})=142 \mathrm{~kJ}[/latex]

The enthalpy of vaporization R-134a at -8°C is [latex]h_{\mathrm{fg}}=204.52 \mathrm{~kJ} / \mathrm{kg}[/latex] (Table A-11). Then the amount of refrigerant that vaporizes during heat absorption becomes

[latex]Q_{L}=m_{ ext {evap }} h_{f g@-8^{\circ} \mathrm{C}} ightarrow m_{ ext {evap }}=\frac{142 \mathrm{~kJ}}{204.52 \mathrm{~kJ} / \mathrm{kg}}=0.694 \mathrm{~kg}[/latex]

Therefore, the fraction of mass that vaporized during heat addition process to the refrigerant is

[latex] ext { Mass fraction }=\frac{m_{ ext {evap }}}{m_{ ext {total }}}=\frac{0.694 \mathrm{~kg}}{0.8 \mathrm{~kg}}=0.868 ext { or } 86.8 \%[/latex]

The pressure at the end of heat rejection process is simply the saturation pressure at heat rejection temperature,

[latex]P_{4}=P_{ ext {sat } @{20^{\circ} \mathrm{C}}}=572.1 \mathrm{kPa}[/latex]

Discussion Carnot cycle is an idealized refrigeration cycle, thus it cannot be achieved in practice. Practical refrigeration cycles are analyzed in Chap. 11.

Question 6.6: A Carnot Refrigeration Cycle Operating in the Saturation Dom...

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