Boyle's Law states that when a sample of gas is compressed at a constant temperature, the pressure P and volume V satisfy the equation PV = C, where C is a constant. Suppose that at a certain instant the volume is 700 cm3, the pressure is 140 kPa, and the pressure is increasing at a rate of 20 kPa/min. At what rate is the volume decreasing at this instant?

To solve this problem, we can use the method of related rates in calculus. Here are the steps:

1. Write down the equation: According to Boyle's Law, PV = C, where P is the pressure, V is the volume, and C is a constant.

2. Differentiate both sides with respect to time (t): Using the product rule for differentiation, the derivative of PV with respect to time is P(dV/dt) + V(dP/dt) = 0, because the derivative of a constant is zero.

3. Substitute the given values: We know that P = 140 kPa, dP/dt = 20 kPa/min, and V = 700 cm^3. We want to find dV/dt. So, we substitute these values into the equation from step 2: 140(dV/dt) + 700(20) = 0.

4. Solve for dV/dt: Rearrange the equation to solve for dV/dt: dV/dt = -700(20) / 140 = -100 cm^3/min.

So, the volume is decreasing at a rate of 100 cm^3/min at this instant.