air expands adiabatically in accordance with the law PV =cost. pound per square inches ,at what rate is pressure changing when the volume is decreasing 1 cubic per second?
To find the rate at which pressure is changing when the volume is decreasing by 1 cubic inch per second, we can differentiate the equation PV = constant, with respect to time.
Step 1: Differentiate PV = constant with respect to time (t), assuming both P and V are functions of time:
(PV)' = (constant)'
Step 2: Apply the product rule of differentiation:
P'(V) + V'(P) = 0
Step 3: Solve for P' (the rate of change of pressure):
P' = -V'(P) / V
Step 4: Substitute the given values:
We need the values of V'(volume rate of change) and V(volume) to calculate P'(pressure rate of change).
However, this equation alone is not enough to determine P' without knowing the specific values of V'(volume rate of change) and V(volume). Please provide the values of V'(volume rate of change) and V(volume) to find the rate at which pressure is changing.