To calculate the electrical energy used by the light bulb and the energy converted into radiant energy, we can use the following formulas:
(a) Electrical Energy Used
Electrical energy (in watt-hours) can be calculated using the formula:
\[ \text{Energy} = \text{Power} \times \text{Time} \]
Where:
- Power = 60 W
- Time = 8.0 hours
Now substituting the values:
\[ \text{Energy} = 60 , \text{W} \times 8.0 , \text{h} = 480 , \text{Wh} \]
To convert watt-hours to joules (since 1 Wh = 3600 J):
\[ 480 , \text{Wh} = 480 \times 3600 = 1,728,000 , \text{J} \]
So, the electrical energy used is 1,728,000 J or 1.728 MJ.
(b) Electrical Energy Converted into Radiant Energy
If the light bulb is only 15% efficient, we can calculate the radiant energy using the efficiency formula:
\[ \text{Radiant Energy} = \text{Efficiency} \times \text{Total Energy} \]
Where:
- Efficiency = 0.15 (15%)
- Total Energy = 1,728,000 J (from part a)
Now substituting the values:
\[ \text{Radiant Energy} = 0.15 \times 1,728,000 , \text{J} = 259,200 , \text{J} \]
Thus, the electrical energy converted into radiant energy (light) is 259,200 J or 259.2 kJ.
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