A competing technology uses a photovoltaic cell to charge a battery which can then be used to power a LED light. To compare these technologies, we make some reasonable assumptions. We assume the solar cell is 10 cm on a side, and that it has an efficiency of 15%. We assume the battery is a LaNi5 nickel metal hydride rechargeable battery with a mass of 50 grams, and we assume that the battery has an actual specific charge of 50% of its theoretical specific charge. We also assume that the battery produces an average voltage of 1.1 V.
d. How much power (in watts) will be generated by our solar cell if we place it in 1000 W/m2 direct incident sunlight? A: 1.5
How much energy can the solar cell produce during a day that receives the equivalent light of 4 hours of 1000 W/m2 direct incident sunlight, in kJ? A: 21.6
How much energy can the battery store, in kJ?
ANSWER: ??????????????????????????
To determine the amount of energy the battery can store, we need to calculate its capacity.
The specific charge of a battery refers to the amount of charge it can hold per unit mass. The theoretical specific charge of the LaNi5 nickel metal hydride battery is typically around 300 mAh/g (milliampere-hour per gram). However, we know that the battery has an actual specific charge of 50% of its theoretical specific charge.
First, let's calculate the theoretical specific charge of the battery using its mass of 50 grams:
Theoretical specific charge = 300 mAh/g * 50 g
Theoretical specific charge = 15000 mAh
Since we need the capacity in ampere-hours (Ah), we have to convert milliampere-hours to ampere-hours by dividing by 1000:
Theoretical specific charge = 15000 mAh / 1000
Theoretical specific charge = 15 Ah
Now, we can calculate the energy the battery can store by multiplying the specific charge by the battery's voltage:
Energy stored in battery = Specific charge * Voltage
Energy stored in battery = 15 Ah * 1.1 V
Finally, we can convert this energy value to kilojoules (kJ) by using the conversion factor 1 Wh = 3.6 kJ:
Energy stored in battery = (15 Ah * 1.1 V) / 1000 * 3.6 kJ
Energy stored in battery ≈ 0.0594 kJ
Therefore, the battery can store approximately 0.0594 kilojoules (kJ) of energy.