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 2L, the pressure is 100 kPa, and the pressure is decreasing at the rate of 5 kPa/sec. Find the rate at which the volume is changing.
A) 14 L/sec
B) $C-$ 14 L/sec
C) $C-$ $\frac{1}{14}$ L/sec
D) $\frac{1}{14}$ L/sec

Question

Quizplus · Accepted Answer

Using the given equation $p^{5} V^{7}=C$, differentiate both sides with respect to time to find the rate of change of volume. Solving the resulting equation gives the rate of change of volume as $\frac{1}{14}$ L/sec.

In an Adiabatic Process (One in Which No Heat Transfer p5V7=Cp^{5} V^{7}=Cp5V7=C

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