One mole of an ideal gas satisfies with and

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

Problem

One mole of an ideal gas satisfies

PV=nRT

with

n=1\text{ mol}

and

R=8.314\text{ kPa}\cdot\text{L}/(\text{mol}\cdot\text{K})

. At a certain instant the gas has pressure

100\text{ kPa}

, volume

2.0\text{ L}

, and temperature

300\text{ K}

. The temperature is increasing at

1\text{ K/s}

while the volume is decreasing at

0.010\text{ L/s}

. What is the instantaneous rate of change of the pressure at that instant? (a)

5.16\,\text{kPa/s}

(b)

4.16\,\text{kPa/s}

(c)

4.66\,\text{kPa/s}

(d)

9.31\,\text{kPa/s}