Question

When air expands adiabatically (without gaining or losing heat), its pressure P and volume V are related by the equation PV^{1.4}=C where C is a constant. Suppose that at a certain instant the volume is 530 cubic centimeters and the pressure is 97 kPa and is decreasing at a rate of 10 kPa/minute. At what rate in cubic centimeters per minute is the volume increasing at this instant?

(Pa stands for Pascal -- it is equivalent to one Newton/(meter squared); kPa is a kiloPascal or 1000 Pascals. )

Answer 1

V^1.4 = C/P

1.4 V^.4 dV/dt = (C/P^2)dP/dt

1.4 (530)^.4 dV/dt = (C/97^2)(10)

get C from initial condition
C = 97 * 530^1.4

Answer 2

the answer is shown to be incorrect....

Answer 3

Actually he forgot to convert the kpa(1000 * N/m^2) into 1000 * N/cm^2