Mathematics

Mathematics

Problem

For a certain gas, pressure

P

(in kPa) depends on volume

V

(in L) by a differentiable, invertible function

P=q(V)

. At

V=2

L,

P=100

kPa and

\dfrac{dP}{dV}=-40

kPa/L. Volume in turn depends on temperature

\theta

(in

^{\circ}\!\text{C}

) through a differentiable, invertible function

V=r(\theta)

with

r(300)=2

and

\dfrac{dV}{d\theta}=0.01

L/°C at

\theta=300\,^{\circ}\!\text{C}

. What is

\dfrac{d\theta}{dP}

at

P=100

kPa? a)

-0.025\;^{\circ}\!\text{C}\!/\!\text{kPa}

b)

-0.4\;^{\circ}\!\text{C}\!/\!\text{kPa}

c)

-2.5\;^{\circ}\!\text{C}\!/\!\text{kPa}

d)

2.5\;^{\circ}\!\text{C}\!/\!\text{kPa}

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