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Problem On page 216: A battery and lightbulb lose about 1 ×10-20 g/s by radiating the equivalent amount of energy into the space that surrounds it. For how many hours will this bulb have to operate at that rate for a measurable amount of mass to have radiated away if the limit of your ability to measure mass is 10-6 g?
Subject Mass and energy, Fine: pages 165-172.
Solution If we look at the units of the specified quantities, and at the what we want to know (a time), we find that actually, to solve this problem, no special equations are needed. If we divide the minimum amount measurable (units: [g]) by the rate of mass loss (units [g/s]), we get:
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minimum measurable mass loss [g]
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= required operating time [s]. |
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Which is the thing we need to know, only in seconds instead of in hours. If we now realize that 1 hour = 3600. s, we can obtain the operating time in hours. Filling in:
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1 ×10-6 [g]
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= 1014 s = 3 ×1010 h. |
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Note that this is a few (about 3) million years.
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