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Chapter 8: Q 636. (page 1031)

The volume of a gas in a container varies inversely with the pressure on the gas. If a container of nitrogen has a volume of 29.5 liters with 2000 psi, what is the volume if the tank has a 14.7 psi rating? Round to the nearest whole number.

Short Answer

Expert verified

The volume will be鈮�4014.

Step by step solution

01

Step 1. Given information.

The volume of a gas in a container varies inversely with the pressure on the gas.

A container of nitrogen has a volume of 29.5 liters with 2000 psi.

Let's take v=the volume of gas.

And p=the price of the gas.

g=the number of gallons bought.

v=29.5whenp=2000

02

Step 2. Write the formula for inverse variation and substitute given values.

The inverse variation formula is y=kx.

we will use vin place of yand pin place of x.

v=kp

Now substitute the given values for the variable,

role="math" localid="1648892841837" 29.5=k200029.5路2000=k59000=k

Rewrite the general equation with the value we found for k,

v=59000p

Now find vwhenp=14.7,

v=59000pv=5900014.7v鈮�4014

If the tank has a 14.7 psi rating then its volume will be around4014.

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