College Algebra, Chapter 2, 2.5, Section 2.5, Problem 32

The Boyle's Law states that the pressure $P$ of a sample gas is directly proportional to the temperature $T$ and inversely proportional to the volume $V$.
a.) Write an equation that expresses this relationship.
$\displaystyle P = \frac{kT}{V}$

b.) Find the constant of proportionality if $100 L$ of gas exerts a pressure of $332 kPa$ at a temperature of $400 K$.

$\begin{equation} \begin{aligned} 33.2 kPa &= \frac{k(400K)}{100L} && \text{Solve for } k\\ \\ k &= 8.3 \frac{kPa \times L }{K} \end{aligned} \end{equation}$


c.) If the temperature is increased to $500K$ and the volume is decreased to $80 L$. What is the pressure of the gas?

$\begin{equation} \begin{aligned} P &= \frac{kT}{V} && \text{Model}\\ \\ P &= \frac{\left( 8.3 \frac{kPa \times L }{K} \right)(500 K)}{(80 L)} && \text{Cancel out like terms, solve for } P\\ \\ P &= 51.875 kPa \end{aligned} \end{equation}$