   Chapter 2.8, Problem 38E

Chapter
Section
Textbook Problem

# When air expands adiabatically (without gaining or losing heat), its pressure P and volume V are related by the equation P V 1.4 = C , where C is a constant. Suppose that at a certain instant the volume is 400 c m 3 and the pressure is 80 kPa and is decreasing at a rate of 10 kPa/min. At what rate is the volume increasing at this instant?

To determine

To find:

The rate at which the volume is increasing

Explanation

1. Concept:

Using the given formula and differentiation, we can find the rate of change of volume

2. Formulae:

i. PV1.4= C, where c is constant.

ii. Product rule of differentiation: ddxfx*gx=fx*ddxgx+gx*ddxfx

iii. Power rule of differentiation: ddxxn=n*xn-1

iv. Chain rule of differentiation: ddtfx=ddxfx*dxdt

3

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