SOLUTION: For a given mass of gas in a piston, 𝑝𝑉1.5 = 400 where p is the pressure in N/m2, and V is the volume in m3. Suppose the pressure increases at a constant rate of 3
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Question 1105904: For a given mass of gas in a piston, 𝑝𝑉1.5 = 400 where p is the pressure in N/m2, and V is the volume in m3. Suppose the pressure increases at a constant rate of 3N/m2 per minute. Find the rate at which the volume is changing at the instant when the pressure is 50N/m2.
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
𝑝𝑉1.5 = 400
:
solve the equation for V
:
V = 266.6667 * p^-1
:
we are looking for the rate the volume is changing dV/dt
:
we know p is increasing at the rate of dp/dt = 3N/m^2, p = 50N/m^2
:
dV/dt = 266.6667 * p^-2 * dp/dt
:
substitute dp/dt = 3, p = 50
:
dV/dt = (266.6667 * 3) / 50^2 = 0.32m^3/minute
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