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What is the available energy content, in joules, of a battery that operates a 2.00-W electric clock for 18 months?

How long can a battery that can supply 8.00×10⁴ J run a pocket calculator that consumes energy at the rate of 1.00×10^−3 W?

A. (a) 4.25 × 10⁷ J, (b) 6.12 × 10⁷ s
B. (a) 4.25 × 10⁷ J, (b) 8.00 × 10⁴ s
C. (a) 7.89 × 10⁵ J, (b) 6.12 × 10⁷ s
D. (a) 7.89 × 10⁵ J, (b) 8.00 × 10⁴ s

User Jlembke
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1 Answer

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Final answer:

The energy content for a 2.00-W clock run over 18 months was incorrectly matched with any option provided; it should be 93,312,000 J. A battery with an energy supply of 8.00×104 J can run a 1.00×10−3 W pocket calculator for 8.00×107 seconds. Solar cells are suitable for low-energy devices like calculators. Thus, the correct answer in part (b) is 8.00×107 seconds.

Step-by-step explanation:

To determine the available energy content of a battery that operates a 2.00-W electric clock for 18 months, we need to calculate:

Energy (E) = Power (P) × Time (t)

First, we convert 18 months into seconds:

18 months × (30 days/month) × (24 hours/day) × (60 minutes/hour) × (60 seconds/minute) = 18 × 30 × 24 × 60 × 60 = 46,656,000 seconds (s)

Then:

E = 2.00 W × 46,656,000 s = 93,312,000 J

However, none of the given options match this calculation. It appears there might be a mistake in either the question or the options provided.

Next, we determine how long a battery with an energy supply of 8.00×104 J can run a pocket calculator that consumes 1.00×10−3 W:

t = E / P

t = 8.00×104 J / 1.00×10−3 W = 8.00×107 s

Thus, the correct answer in part (b) is 8.00×107 seconds.

For the discussion about the ability of solar cells to run different devices, we note that they are suitable for low-energy consuming devices like calculators, but not sufficient to start internal combustion engines in cars and trucks.

User Jack White
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