Question

The volume of gas varies directly with temperature and inversely with pressure. Volume is 100m^3 when temperature is 1508 degrees and pressure is 15 lb/cm^2. What is the volume when the temperature is 2508 degrees and the pressure is 20 lb/cm^2?
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Answer 1

Let's begin by restating the word problem as an equation.
"The volume of gas varies directly with temperature" means \[V \alpha T\]
"[The volume of gas varies] inversely with pressure" means \[V \alpha 1/P\]
We can combine this and write what is known as the Combined Gas Law: \[\frac{P _{1} V _{1}}{ T _{1} }=\frac{P _{2} V _{2}}{ T _{2} }\]
Note that this is only true for an ideal gas. Since we've been given the relations, we an assume that it is an ideal gas and plug into the equation without any modifications. Because we maintain units across the ratio, we can get away with mixing metric and imperial units, but it's usually a better idea to work with one or the other. Plugging in:
\[\frac{15 * 100}{ 1508 }=\frac{20 * V _{2}}{ 2508 }\]
Now just solve for the final volume.

Answer 2

I don't know how

Answer 3

You want to isolate V2

Answer 4

@ReviewerC after i multiply 15 and 100 what do i do?

Answer 5

@Mertsj

Answer 6

@jim_thompson5910 Can you help me with this one too?

Answer 7

\[\large \frac{15 * 100}{ 1508 }=\frac{20 * V _{2}}{ 2508 }\]


\[\large \frac{1500}{ 1508 }=\frac{20V_{2}}{ 2508 }\]


\[\large 1500*2508 = 1508*20V_{2}\]


\[\large 3762000 = 30160V_{2}\]


\[\large \frac{3762000}{30160} = V_{2}\]


\[\large 124.734748 = V_{2}\]


\[\large V_{2} = 124.734748\]

Answer 8

Thanks, can I just tag you in any question that I need help with?

Answer 9

sure, but I can only do a few though, not all

Answer 10

ok Thank You so much.

Answer 11

yw