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 420 cubic centimeters and the pressure is 99 kPa and is decreasing at a rate of 7 kPa/minute. At what rate in cubic centimeters per minute is the volume increasing at this instant?

Explanation:

We are given that

Where C=Constant

V=420 cubic cm and P=99KPa

We have to find the rate at which the  volume increasing at this instant.

Differentiate w.r.t t

Substitute the values

Explanation:

Given:

initial pressure during adiabatic expansion of air,

initial volume during the process,

The adiabatic process is governed by the relation ; where C is a constant.

Rate of decrease in pressure,

Then the rate of change in volume, can be determined as:

The rate of change in volume will be increasing.

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