Question

general chemistry 4th edition mcquarrie • rock • gallogly university science books presented by macmillan learning
in a certain city, electricity costs $0.11 per kw·h. what is the annual cost for electricity to power a lamppost for 8.00 h per day with a 100. w incandescent light bulb versus an energy efficient 25 w fluorescent bulb that produces the same amount of light? assume 1 year = 365 days.

1. w bulb: $ /year

25 w bulb: $ /year
a typical incandescent bulb costs $0.89 and lasts for about a year; a typical energy efficient fluorescent bulb costs about $3.49 and lasts for about 3 years.
is the additional cost of the fluorescent bulb justified?
yes
no

Explanation:

Step1: Convert power to kW for 100 - W bulb

$100\ W=\frac{100}{1000}\ kW = 0.1\ kW$

Step2: Calculate annual energy consumption for 100 - W bulb

Annual energy consumption $E_1=0.1\ kW\times8\ h/day\times365\ days = 292\ kW\cdot h$

Step3: Calculate annual cost for 100 - W bulb

Annual cost $C_1 = 292\ kW\cdot h\times0.11\ $/kW\cdot h=\$32.12$

Step4: Convert power to kW for 25 - W bulb

$25\ W=\frac{25}{1000}\ kW=0.025\ kW$

Step5: Calculate annual energy consumption for 25 - W bulb

Annual energy consumption $E_2 = 0.025\ kW\times8\ h/day\times365\ days=73\ kW\cdot h$

Step6: Calculate annual cost for 25 - W bulb

Annual cost $C_2=73\ kW\cdot h\times0.11\ $/kW\cdot h=\$8.03$

Step7: Analyze cost - effectiveness of fluorescent bulb

Over 3 years, cost of incandescent bulbs: $(0.89 + 32.12\times3)=\$97.25$
Over 3 years, cost of fluorescent bulb: $(3.49+8.03\times3)=\$27.58$

Answer:

1. W bulb: $\$32.12$/year

25 W bulb: $\$8.03$/year
yes