25.8 - Sample problem: solar panels
A school in Los Angeles is deciding whether or not to install solar panels on its roof. The photovoltaic system under consideration provides 680
watts of power under direct sunlight, costs $3500, and is expected to last 25 years, according to the experts at Stewart Solar Systems. In Los
Angeles the average insolation, or equivalent hours of direct sunlight reaching the Earth’s surface, is 5.62 hours per day.
(a) How many watt-hours of electricity will the solar panels provide during their lifetime? (A watt-hour is a unit of energy just like the Joule; it is
calculated by multiplying the power and the amount of time that power is produced.)
(b) Suppose the cost of electricity coming from the local utility company is predicted to average $0.11 per kilowatt-hour (kW·h) over the next 25
years. What is the cost per kW·h of the solar panel system over its lifetime? Should the school buy the solar panels?
Variables
What is the strategy?
- Find the total number of hours of direct sunlight the solar panels will receive over their lifetime.
- Calculate the number of watt-hours the solar panels will produce over their lifetime. Convert to kW·h.
- Calculate the price per kW·h from the solar panels and compare it with the utility company’s price.
Physics principles and equations
Power stated as energy used over a period of time
P = ǻE/ǻt
Step-by-step solution
First, find the total amount of energy the solar panels will produce over their lifetime.
This public school uses solar power.
Using information supplied below,
determine how many watt-hours of
electricity the solar panels will provide
during their lifetime.
What will the cost per kW·h of the
solar panel system be over its
lifetime? Suppose the cost of
traditional energy will average $0.11
per kilowatt-hour over the next 25
years. Will the school save money?
generation power of solar panel system P = 680 W
lifetime of system t = 25 y
average equivalent hours of sunlight per day s = 5.62 h/d
equivalent hours of sunlight over system lifetime S
energy produced over system lifetime E
price of utility electricity per kW·h p = $0.11
one-time cost of solar panel system C = $3500
cost of solar panel system per kW·h c