The volume V (in cubic inches) and pressure p (in pounds per
square inch) of a certain gas satis¯es the equation pV = 1000. At what
rate is the volume of the sample changing if the pressure is 100lb=in2
and is increasing at the rate of 2lb=in2 per second?
Well I’m guessing that pV is a constant.
Let’s write pV = k (where k = 1000 for your question)
Then, in terms of p
V= k/p
So as p changes, the rate of change of V is
dV/dp = -k/p²
and you can write the change in volume as
dV = – k dp/p²
=> dV/dt = – k/p² dp/dt
Now just plug in the numbers: p =100, dp/dt = 2/second and k=1000
I get dV/dt = -0.2 (in²/s)
Well I’m guessing that pV is a constant.
Let’s write pV = k (where k = 1000 for your question)
Then, in terms of p
V= k/p
So as p changes, the rate of change of V is
dV/dp = -k/p²
and you can write the change in volume as
dV = – k dp/p²
=> dV/dt = – k/p² dp/dt
Now just plug in the numbers: p =100, dp/dt = 2/second and k=1000
I get dV/dt = -0.2 (in²/s)
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