Answer
$50; Fluorescent lamps are replacing halogen lamps because fluorescent lamps use less energy than halogen lamps. This means that fluorescent lamps are less expensive to operate.
Work Step by Step
The following information is given in the question:
The cost of electricity is \$0.10 per kW $\cdot$ hr; the time is 5 hours a day for a year, and the lamp uses 300-watts of energy. Remember that a watt is a joule per second.
I solved this question in three steps. First, I found the amount of energy used by the lamp, and then the cost of using that amount of energy. Finally, the question asks to comment on the transition from halogen lamps to fluorescent ones so I did that as well.
The amount of energy used by the lamp is calculated using the following series of conversions:
$$ E= (300 W) (3600 s \cdot hr^{-1}) (5 hr \cdot day^{-1}) (365 days) = 1.97 \cdot 10^{9} W. $$
Using the conversion factor $1000 J = 1 kJ$, this is equal to 1.97 $\cdot 10^{6} $kW.
Because a watt is equal to 1 kJ $s^{-1}$ and the cost of electricity is given in kJ $\cdot hr^{-1}$, I use the conversion factor of 3600 seconds is equal to 1 hour to get the energy consumption in kJ $\cdot hr^{-1}$. I get 550 kJ $\cdot hr^{-1}$ as my answer for the first part.
For the second part, I divide the answer to the first part by the cost per kJ $\cdot$
$$ \frac{550 kJ \cdot hr^{-1}}{$0.10 \cdot kW^{-1} } = $55 $$
Thus, $55 is the answer to the second part.
To answer the third part, halogen lamps use more energy than fluorescent lamps which makes them more costly to use. It makes sense that people use the less expensive option in their homes.
