For a fixed amount of an ideal gas

MATHEMATICS · Subjective · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation

Problem

For a fixed amount of an ideal gas, pressure

P

(in atm), volume

V

(in L), and temperature

T

(in K) satisfy

PV=0.0821\,nT

with

n=1\text{ mol}

. At a moment when

P=3.0\text{ atm}

V=10\text{ L}

T=300\text{ K}

, the temperature is rising at

2.0\text{ K/s}

while the volume is decreasing at

0.10\text{ L/s}

. Determine the instantaneous rate of change of the pressure (in atm/s).