At a constant temperature, the volume ( v ) of a gas varies inversely as the pressure ( W ). Translate the statement of variation into an equation and use k as the constant of variation.
A) $W = \frac { k } { v }$
B) $v = \frac { k } { W }$
C) $W = k v$
D) $v = \frac { W } { k }$
E) $k = \frac { W } { v }$

Question

Quizplus · Accepted Answer

The statement "the volume (v) of a gas varies inversely as the pressure (W)" can be translated into the equation v = k/W, where k is the constant of variation. This is because as pressure increases, volume decreases and vice versa. To maintain a constant temperature, the product of pressure and volume must be constant (Boyle's Law). Therefore, when one variable increases, the other must decrease in order to maintain the constant product. Solving for k, we get k = vW. Therefore, the correct equation is v = k/W.

At a Constant Temperature, the Volume ( V ) of a Gas