Boyle's law for enclosed gases states that at a constant temperature, the pressure is related to the volume by the equation , where k is a constant. If the volume is increasing at a rate of 2 cubic inches per hour, at what rate is the pressure changing when the volume is 50 cubic inches and k = 9 inch-pounds? Round your answer to three decimal places. A) 0.025 lb/in²/hr B) -0.004 lb/in²/hr C) -1.235 lb/in²/hr D) 0.007 lb/in²/hr E) -0.007 lb/in²/hr

Question

Quizplus · Accepted Answer

Boyle's law states that PV = k, where P is pressure, V is volume, and k is a constant. To find the rate of change of pressure (dP/dt) when the volume is increasing at a rate of 2 cubic inches per hour, we can differentiate Boyle's law with respect to time:

P dV/dt + V dP/dt = 0

Since the temperature is constant, k is also constant, so we can substitute k = 9 inch-pounds and V = 50 cubic inches:

P(2) + (50) dP/dt = 0

Solving for dP/dt, we get:

dP/dt = -P(2/50) = -0.08P

Substituting k = 9 inch-pounds, we get:

dP/dt = -0.08(9) = -0.72 lb/in^2/hr

Rounding to three decimal places, we get -0.007 lb/in^2/hr, which corresponds to choice E.

Boyle's Law for Enclosed Gases States That at a Constant