Final answer:
To find the outdoor temperature, we must calculate the energy used to maintain inside temperature based on the cost of air vented out, the volume of the house, density of air, and the COP of the air conditioner, and then use the appropriate thermodynamic relations. Therefore the correct answer is D. 23.4°C.
Step-by-step explanation:
The question asks us to determine the outdoor temperature when a house, maintained at 24°C by an air-conditioning system with a COP of 2.9, vents out a certain cost in electricity due to the operation of fans.
The air being vented out is replaced once every hour, and the density of the air is 1.20 kg/m³. Given the volume of the house and the cost of the electricity vented out over 8 hours, we need to find the corresponding outdoor temperature.
Let's calculate the energy required to maintain the inside temperature and the amount 'vented out.' Since the electricity cost for 8 hours is $0.75 and the unit cost is $0.18/kWh, we can find out the total kWh used and then by using the COP, find the energy transferred.
After that, we need to use the thermodynamic relation that equates energy transferred with mass, specific heat capacity, and temperature difference to find the outdoor temperature.