Chapter 12.8, Problem 10OE

To determine

To Describe: Translate the statement into formula:

The pressure, $P$ , of a gas varies directly as its temperature , $T$ , and inversely as its volume, $V$ .

Answer to Problem 10OE

The formula of the statement is $P=K\frac{T}{V}$ .

Explanation of Solution

Given information:

Translate statement to formula:

The pressure, $P$ , of a gas varies directly as its temperature , $T$ , and inversely as its volume, $V$ .

Use $K$ as constant.

Consider the statement,

The pressure, $P$ , of a gas varies directly as its temperature , $T$ , and inversely as its volume, $V$ .

Here if a variable varies directly as he product of two or more other variables the resulting relationship is a joint variation.

As , $P$ ,varies directly to $T$ and inversely to $V$ .

  $P$ is directly as $T$ .

  $P\alpha T$ .

Then $P$ is inversely as its volume $V$ .

  $P\alpha \frac{1}{V}$

From both of the equations:

  $\begin{array}{c}P\alpha T\\ P\alpha \frac{1}{V}\\ P\alpha \frac{T}{V}\end{array}$

Same as above,

Here,

  $P\alpha \frac{T}{V}$

For replacing $\alpha$ apply constant $K$ .

  $\begin{array}{l}P\alpha \frac{T}{V}\\ P=K\frac{T}{V}\end{array}$

Thus, the formula is: $P=K\frac{T}{V}$ .