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Question 1188303: For a given mass of gas in a piston, 𝑝𝑉^1.5 = 400 where p is the pressure in N/m^2, and V is the volume in m^3. Suppose the pressure increases at a constant rate of 3 N/m^2 per minute. Find the rate at which the volume is changing at the instant when the pressure is 50 N/m^2.
Answer by artographer(1)   (Show Source):
You can put this solution on YOUR website! 𝑝𝑉1.5 = 400
Solving the equation for V,
V = 266.6667 * p^-1
Rate the volume dV/dt,
p is increasing at the rate of dp/dt = 3N/m^2, p = 50N/m^2
dV/dt = 266.6667 * p^-2 * dp/dt
Put dp/dt = 3, p = 50
dV/dt = (266.6667 * 3) / 50^2 = 0.32m^3/minute
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