word problem

Question

I need a step by step process for the following problem 

 

When temperature stays the same, the volume of a gas is inversely proportional to the pressure of the gas. If a balloon is filled with 105 cubic inches of a gas at a pressure of 14 lbs per square inch, find the new pressure of the gas if the volume is decreased to 15 cubic inches. 

Answer 1

I did a problem similar to this one with you a few hours ago.  Only this time, the relationship is an inverse one.

 

Let x = volume

Let y = pressure

 

The pressure of a gas depends on its volume because of the dimensions of space in which the volume is contained in.

 

We can write a proportion that describes this relationship.

 

y ∝ 1 / x

 

This means that if volume increases, pressure decreases. The opposite effect also happens.

 

If we add a constant K, we can establish an equation.

 

y = K / x

 

 

Plug in the initial values into the equation to find K.

 

x = 105

y = 14

 

K = xy

K = 105 * 14

K = 1470

 

 

Now we find the pressure of the gas when the volume is 15 cubic inches.  Use the value of K we just found and x=15 into the equation.

 

y = K / x

y = 1470 / 15

y = 98

 

When the volume is 15 cubic inches, the pressure is 98 lbs per square inch.  Lets compare this to the initial conditions.

 

Volume = 105       Pressure = 14

Volume = 15         Pressure = 98

 

 

As you can see when the volume decreases, the pressure increases.  Thus proving the relationship.