1. ## word problem

The volume V of a gas varies inversely as the pressure P upon it. The volume of a gas is 200 cu cm under a pressure of 32kg/sq. cm
a. find the variation constant
b. what will be its volume under a presure of 40 kg/sq. cm

The volume V of a gas varies inversely as the pressure P upon it. The volume of a gas is 200 cu cm under a pressure of 32kg/sq. cm
a. find the variation constant
b. what will be its volume under a presure of 40 kg/sq. cm
Hint: to vary inversly means they have this relationship.

$V = \frac kT$ .........for $k$ some constant (call the proportionality constant)

3. im sorry that made no sense to me lol i am so lost

The volume V of a gas varies inversely as the pressure P upon it. The volume of a gas is 200 cu cm under a pressure of 32kg/sq. cm
a. find the variation constant
b. what will be its volume under a presure of 40 kg/sq. cm
I think Jhevon should have wrote it as:

$V = \frac{k}{P}$

Where $V$ is the volume and $P$ the pressure.

In the first question, to find the constant $k$ you need to put the given values for $V$ and $P$ in the equation, and solve for $k$.

In the second question you now make use of that value for $k$ when solving for the volume, $V$.

5. Originally Posted by janvdl
I think Jhevon should have wrote it as:

$V = \frac{k}{P}$

Where $V$ is the volume and $P$ the pressure.

In the first question, to find the constant $k$ you need to put the given values for $V$ and $P$ in the equation, and solve for $k$.

In the second question you know make use of that value for $k$ when solving for the volume, $V$.
yes, i meant P not T

6. i am confused how to solve for k

7. As janvdl said, substitute in the given values of V and P and solve for k.

$
200 = \frac{k}{32}
$

Solve for k, multiply both sides by 32.

8. 32*200=6400 is that the value of k

32*200=6400 is that the value of k
Yes. Now use that value for $k$ and the given value for $P$, to solve for $V$. (The second question.)

10. Yes so you have the proportionality formula:

$
V = \frac{6400}{P}
$

To find V when P = 40, substutute P = 40 into the formula.

11. so the volume in the second one owuld equal 160