One mole of an ideal gas is confined in a cylinder with a movable piston

MATHEMATICS · Multi-part · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation

Problem

One mole of an ideal gas is confined in a cylinder with a movable piston. The absolute temperature of the gas is held fixed at

T=300\text{ K}

. The pressure

P(t)

of the gas is increasing at a rate of

0.050\text{ kPa/s}

when the pressure is

120\text{ kPa}

. (1) Calculate the instantaneous rate at which the volume

V(t)

of the gas is changing at that moment. Express your answer with correct units. (2) State whether the volume is increasing or decreasing and justify your conclusion based on your calculation.

Related theory

Algebraic Proportion
Rates of Change

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