## Related questions with answers

An office building requires a heat transfer rate of $20\ \mathrm{kW}$ to maintain the inside temperature at $21^{\circ} \mathrm{C}$ when the outside temperature is $0^{\circ} \mathrm{C}$. A vapor-compression heat pump with Refrigerant $22\mathrm{a}$ as the working fluid is to be used to provide the necessary heating. The compressor operates adiabatically with an isentropic efficiency of $82 \%$. Specify appropriate evaporator and condenser pressures of a cycle for this purpose assuming $\Delta T_{\text {cond }}=\Delta T_{\text {cvap }}=10^{\circ} \mathrm{C}$, as shown in figure. The states are numbered as in figure. The refrigerant exits the evaporator as saturated vapor and exits the condenser as saturated liquid at the respective pressures. Determine the (a) mass flow rate of refrigerant, in $\mathrm{kg} / \mathrm{s}$. (b) compressor power, in $\mathrm{kW}$. (c) coefficient of performance and compare with the coefficient of performance for a Carnot heat pump cycle operating between reservoirs at the inside and outside temperatures, respectively.. Compare the results with those of previous problem and discuss.

Solution

Verified$T_1=0-10=-10\,\mathrm{\circ C}=T_{evap}$

From Table A-7: $p_1=3.5485$ bar, $h_1=246.15\,\mathrm{\frac{kJ}{kg}}$, $s_1=s_{2s}=0.9424\,\mathrm{\frac{kJ}{kgK}}$

$T_3=21+10=31\,\mathrm{\circ C}$

Interpolation in Table A-7 gives $p_3=12.245$ bar, $h_3=h_4=176.23\,\mathrm{\frac{kJ}{kg}}$

Table A-9 gives: $h_{2s}=276.14 \,\mathrm{\frac{kJ}{kg}}$

$h_2=\frac{h_{2s}-h_1}{\eta _c}+h_1=281.02\,\mathrm{\frac{kJ}{kg}}$

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