Boyle’s law states that if the temperature of an ideal gas is held constant, then the pressure p of the gas and its volume v sat
isfy the relationship p=kv, where k is a constant. 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?.
The best answer that describes the relationship between the rate of change with respect to time of the pressure and the rate of change with respect to time t of the volume is; dP/dt = (-k/V²)(dV/dt)
We are given;
p = k/v
Thus if we cross multiply, we will get;
PV = k
Where;
P is pressure
V is volume
k is a constant
Using the product rule of differentiation on both sides with respect to time t gives;
V(dP/dt) + P(dV/dt) = 0
This is because k is a constant.
Putting k/v for P gives;
V(dP/dt) + (k/V)(dV/dt) = 0
>> V(dP/dt) = - (k/V)(dV/dt)
Divide both sides by V by division property ofequality to get;
