In an Adiabatic Process (One in Which No Heat Transfer $P ^ { 5 } V ^ { 7 } = C$

Multiple Choice

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.

A) $14 \mathrm {~L} / \mathrm { sec }$
B) $C - 14 \mathrm {~L} / \mathrm { sec }$
C) $C - \frac { 1 } { 14 } \mathrm {~L} / \mathrm { sec }$
D) $\frac { 1 } { 14 } \mathrm {~L} / \mathrm { sec }$