Consider the case is which the volume and temperature of ONE mole of an ideal gas depends explicitly on the time, t. obtain an equation (a differential equation essentially) that relates the rate of change in the pressure to the rate of change of the volume and the temperature.

Than consider the scenario in which the temperature is cooling exponentially toward absolute zero with time constant
\(\tau_{T}\)

. ( This is known as Newtonian cooling) Simultaneously the piston is being driven in so that the volume decreases exponentially to zero with a time constant

\(\tau_{V}\)

. Obtain an expression for the rate at which the pressure changes in this case. What is the time dependence of pressure when
\(\tau_{T}=\tau_{V}\)