Question

When air expands adiabatically (without gaining or losing heat), its pressure P and volume V are related by the equation PX‰¹.4=¶, where ¶ is a constant. Suppose that at a certain instant the volume is 450cm³ and the pressure is 65kPa and is decreasing at a rate of 4kPa/min. At what rate is the volume increasing at this instant?

Answer 1

To find the rate at which the volume is increasing during an adiabatic expansion of air, we need to use the equation PX^1.4=C and differentiate it with respect to time.

Step-by-step explanation:

In this problem, we have an adiabatic expansion of air, which can be described by the equation PX1.4=C, where C is a constant.

To find the rate at which the volume is increasing, we need to differentiate this equation with respect to time.

First, we differentiate both sides of the equation with respect to time:

(dP/dt)X1.4+1.4PX0.4(dX/dt)=0

Then, we substitute the given values: P=65 kPa, X=450 cm³, and (dP/dt)=-4 kPa/min.

After substituting these values, we can solve for (dX/dt) to find the rate at which the volume is increasing.