For a weather balloon the variables pressure (kPa)

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

Problem

For a weather balloon the variables pressure

P

(kPa), volume

V

(L), amount of gas

n

(mol), and temperature

T

(K) satisfy the ideal-gas relationship. At a particular instant the values are

P = 90\text{ kPa}

V = 30\text{ L}

, and

T = 300\text{ K}

. The temperature is increasing at

1.0\text{ K/s}

, the balloon is expanding at

0.20\text{ L/s}

, and gas is leaking out at

0.002\text{ mol/s}

. What is the instantaneous rate of change of the pressure,

dP/dt

, at that instant? (a)

+0.30\text{ kPa/s}

(b)

+0.47\text{ kPa/s}

(c)

-0.47\text{ kPa/s}

(d)

-0.30\text{ kPa/s}