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3 years ago

9

Lesson 14.2 Interpret graph boyles law

1 answer:

docker41 [41]3 years ago

6 0

As what we can see on the graph of the Boyle's Law, we can imply that volume and pressure are inversely proportional. The gas law furthermore explains that at this condition, the temperature must be held constant. The law can be furthermore be explained using the equation:

PV = k

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$C(t)=\frac{r}{k}-(\frac{r-kC_o}{k})e^{-kt}$

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The differential equation is given as:

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Taking integral of both sides; we have:

$\int\limits \frac{dC}{r- kC} = \int\limits dt$

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$r-kC=e^{-kt-kD}$

$r-kC=e^{-kt}e^{-kD}$

$r-kC=Ae^{-kt}$

$kC=r-Ae^{-kt}$

$C=\frac{r}{k}-\frac{A}{k}e^{-kt}$

$C(t)=\frac{r}{k}-\frac{A}{k}e^{-kt}$ ------- equation (1)

If C(0)= $C_o$ ; we have:

C(0)= $\frac{r}{k}-\frac{A}{k}e^0$ (where; A is an integration constant)

$C_o = \frac{r}{k}- \frac{A}{k}$

$C_o=\frac{r-A}{k}$

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$A=r-kC_o$

Substituting $A=r-kC_o$ into equation (1); we have;

$C(t)=\frac{r}{k}-(\frac{r-kC_o}{k})e^{-kt}$

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