For an ideal gas kept at constant temperature and fixed amount of gas

MATHEMATICS · Single correct · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation

Problem

For an ideal gas kept at constant temperature and fixed amount of gas, the pressure

P

and volume

V

satisfy

PV=k

for some constant

k

. At a particular instant the volume of the gas is decreasing. Which of the following best describes the instantaneous rate of change of the pressure

\dfrac{dP}{dt}

at that instant? (a)

\dfrac{dP}{dt}

is negative because pressure decreases as volume decreases. (b)

\dfrac{dP}{dt}

cannot be determined without the current value of

V

. (c)

\dfrac{dP}{dt}

is positive because pressure increases as volume decreases. (d)

\dfrac{dP}{dt}=0

because

PV

is constant.