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When air expands adiabatically (without gaining or losing heat), its pressure P and volume V are related by the equation PV1.4=C where C is a constant.
Suppose that at a certain instant the volume is 600 cubic centimeters and the pressure is 75 kPa and is decreasing at a rate of 14 kPa/minute.
At what rate in cubic centimeters per minute is the volume increasing at this instant?
cm3min
Note: Pa stands for Pascal -- it is equivalent to one Newton/(meter squared); kPa is a kiloPascal or 1000 Pascals.
To solve this problem, you'll need to use implicit differentiation on the equation PV1.4=C. Remember, even though C is constant, both P and V are changing with respect to time. After differentiating, you'll need to substitute the given values for P, V, and dPdt to find dVdt. Pay attention to the units and make sure your final answer is in cubic centimeters per minute.
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Box 1: Enter your answer as a number (like 5, -3, 2.2172) or as a calculation (like 5/3, 2^3, 5+4)
Enter DNE for Does Not Exist, oo for Infinity
80