In a sealed vessel of fixed volume

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

Problem

In a sealed vessel of fixed volume, the pressure

P

(in kPa) of a gas is

P = 8.31\,T

, where the temperature

T

(in K) varies with time

t

(in minutes) according to

T = 300 + 4t - 0.1t^{2}

for

0\le t\le40

. At what time is the pressure increasing at

20

kPa per minute? (a)

12\text{ min}

(b)

8\text{ min}

(c)

20\text{ min}

(d)

16\text{ min}