Calculus - question

Question

When air expands 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 cm3 and the pressure is 80 kiloPascals(kPa) and is decreasing at a rate of 10 kiloPascals per minute. Find the rate of change of the volume at this instant. Write the answer in a sentence to indicate its meaning of the context of the problem.

Answer 1

Hi,

P V 1.4 = C

dp/dt * v + dv/dt *p = 0

as you know v = 400 p = 80 and dp/dt = -10 (because decreasing)

dp/dt * v + dv/dt *p = 0

(-10) * 400 + dv/dt * 80 = 0

dv/dt = 50 it means volume will be increasing by rate as 50 Cm³/ per minutes

I hope it is useful,

Minoo