Question

Which of the following best describes the relationship between the rate of change, with respect to time t, of the pressure and the rate of change, with respect to time t, of the volume?

a) dP/dt = k/(dV/dt)
b) dP/dt = -k/(dV/dt)
c) dP/dt = k/V^2 (dV/dt)
d) dP/dt = -k/V^2 (dV/dt)

Please choose the correct option that describes the relationship between the rate of change of pressure and volume.

Answer 1

The correct relationship between the rate of change of pressure and volume is given by Boyle's law as dP/dt = -k/V^2 (dV/dt) since pressure and volume of a gas have an inverse relationship at constant temperature.

Step-by-step explanation:

The relationship between the rate of change of pressure with respect to time (dP/dt) and the rate of change of volume with respect to time (dV/dt) in the context of Boyle's Law can be deduced from the fact that pressure and volume have an inverse relationship at a constant temperature and amount of gas. Boyle's law states that PV = k where k is a constant. This means that as the pressure increases, the volume decreases and vice versa, which is mathematically represented as P×1/V or P à 1/V.

When considering the rates of change, we know that if P increases, V must decrease, and the rate of change of volume with respect to time would have an opposite sign to the rate of change of pressure with respect to time. Therefore, we can express this as dP/dt = -k/V² (dV/dt), where -k/V² reflects the inverse proportionality. Option (d) is the correct answer: dP/dt = -k/V² (dV/dt).