A filament lamp-
cost- 80p
effiency- 0.2
expected life- 1000 hours
a compact fluorescent lamp (CFL)-
cost- £3.00
effiency- 0.8
expected life- 8000 hours
a filament lamp with a power rating of 100W gives 2000 units of light.
what power rating would a CFL need to provide 2000 units of light?
a)8000W
b)20W
c)25W
d025W
To determine the power rating required for a CFL to provide 2000 units of light, we need to compare the efficiencies of the two types of lamps. The efficiency is the ratio of the useful output energy (light) to the input energy (power).
First, let's determine the efficiency of the filament lamp. It is given that its efficiency is 0.2, which means it converts 20% of the input energy into light. Therefore, the filament lamp would require 100W of power to produce 2000 units of light.
Now, let's calculate the power rating needed for the CFL to achieve the same output. We can use the efficiency of the CFL, which is given as 0.8. Rearranging the efficiency equation, we get:
Efficiency = (Useful Output Energy / Input Energy)
0.8 = (2000 units of light / Input Energy)
Rearranging the equation to solve for Input Energy, we have:
Input Energy = 2000 units of light / 0.8
Input Energy = 2500 units of light
Now, since the CFL is expected to provide the same amount of light as the filament lamp (2000 units of light), we can determine the power rating needed for the CFL to achieve this output. Given that Input Energy = Power x Time, the equation becomes:
2500 units of light = Power x Time
Substituting the expected life of the CFL (8000 hours) for Time, we get:
2500 units of light = Power x 8000 hours
Solving for Power:
Power = 2500 units of light / 8000 hours
Power ≈ 0.3125 units of light per hour
To convert the power from units of light per hour to watts, we can multiply by the power rating of the filament lamp (100W):
Power ≈ 0.3125 units of light per hour x 100W
Power ≈ 31.25W
Therefore, the power rating needed for the CFL to provide 2000 units of light is approximately 31.25W.
The correct answer is c) 31W.