Final answer:
For a newer residential split system air conditioner, you would expect to find it charged with R-410A. The effective resistance of a 50 kW air conditioner operating at 408 V is 3.34 Ω. Running it for 240 hours in a month at the cost of 9 cents/kW·h would amount to a cost of $1080.
Step-by-step explanation:
When servicing a newer residential split system air conditioner, you would expect to find the system charged with refrigerant R-410A. This refrigerant has become the standard for residential and commercial air conditioners in recent years, replacing older refrigerants such as R-22 due to its lower environmental impact and higher efficiency.
Calculation of Effective Resistance
The effective resistance (R) of an air conditioner can be calculated using the formula P = V2/R, where P is the power consumption and V is the voltage. In this case,
P = 50.0 kW = 50,000 W
V = 408 V
R = V2/P = (408 V)2/50,000 W = 3.34 Ω
Cost of Running the Air Conditioner
To calculate the cost of running the air conditioner during a hot summer month:
- Calculate the total hours of operation: 8.00 h per day × 30 days = 240 h.
- Calculate the total energy consumption: 50.0 kW × 240 h = 12,000 kW·h.
- Calculate the cost: 12,000 kW·h × $0.09/kW·h = $1080.
Therefore, the cost of running the air conditioner for one month would be $1080.