Problem

A gas occupies 6.52 liters at a pressure of 0.92 atmospheres. Determine the volume if the pressure is increased to 1.44 atmospheres. If the pressure change is linear and occurs over a period of 5 seconds, what is the instantaneous rate of change of the volume with respect to time at 2 seconds?

Solution

so we have

Therefore the value of C is 5.9984, in units of atmosphere-liters. When the pressure increases to 1.44 atmospheres, the new volume will be

We know that the pressure change is linear, so we can write explicitly a formula for the pressure as a function of time:

dP/dt and dV/dt are related by the formula from example 1,

We compute dP/dt, then substitute for P(t) to find dV/dt.