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Answer:
The gas is decreasing at a rate of 50 cubic centimeters per minute.
Explanation:
The Boyle's Law is represented by the following expression:
(1)
Where:
- Pressure, in kilopascals.
- Volume, in cubic centimeters.
- Proportionality constant, in kilopascal-cubic centimeters.
By definitions of rate of change and implicit differentiation, we derive the following differential equation:
(2)
Where:
- Rate of change of the pressure, in kilopascals per minute.
- Rate of change of the volume, in cubic centimeters per minute.
Then, we clear the rate of change of the volume within (2):
If we know that ,
and
, then the rate of change of the volume is:
The gas is decreasing at a rate of 50 cubic centimeters per minute.