Question

A combined heat-engine and air-conditioning system is planned for a shopping center. Concentrated solar energy will be used to maintain a high-temperature reservoir at 500°C, rejecting the heat to an environment with an average summer temperature of 31°C. The center has a total area of 1.0 million sq. ft. and will be maintained at 18°C. Heat accumulation from heat transfer into the building, heat generation by occupants and lighting, as well as other energy dissipations need to be removed in order to maintain the desired temperature. Design calculations show that a heat removal rate of about 3 W/sq. ft. is required.
Determine

a) the minimum net power needed by the air-conditioner;

b) the minimum thermal power to be supplied by the solar collector to the heat engine, if all the net power output is used to power the air-conditioning unit.

Answer 1

Answer:

(a) $3*10^{6} W$

(b) $4.9447*10^{6} W$

Explanation:

(a)

Minimum power to maintain desired temperature is given by

$P_{min}=\frac {3W}{sq.ft} \times A=\frac {3W}{sq.ft} 1*10^{6} sq.ft=3*10^{6} W$

(b)

Efficiency of heat engine

Converting temperature to Kelvin

T1=31 degrees=31+273=304 K

T2=500 degree=500+273=773

$Effieciency=1-\frac {T1}{T2}=1-\frac {304 K}{773 K}=0.6067$

Considering required output of $3*10^{6} W$ then the power needed to be supplied by the solar collector to heat engine is given by

$P_{solar}=\frac {P_{min}}{Efficiency}=\frac {3*10^{6}}{0.6067}=4.9447*10^{6} W$