In an Adiabatic Process (One in Which No Heat Transfer $P$

Short Answer

In an adiabatic process (one in which no heat transfer takes place), the pressure $P$ and volume $V$ of an ideal gas such as oxygen satisfy the equation
$$P ^ { 5 } V ^ { 7 } = C$$
where $C$ is a constant. Suppose that at a certain instant of time, the volume of the gas is $2 \mathrm {~L}$ , the pressure is $100 \mathrm { kPa }$ , and the pressure is decreasing at the rate of $5 \mathrm { kPa } / \mathrm { sec }$ . Find the rate at which the volume is changing.