Question

The volume of gas varies directly as the temperature and inversely as the pressure. If the volume is 150 cubic centimeters when the temperature is 320ºK (Kelvin) and the pressure is 15 pounds per square centimeter, what is the volume when the temperature is 260 ºK and the pressure is 40 pounds per square centimeter?

Answer 1

V1 = 150
T1 = 320
P1 = 15

V2 = ?
T2 = 260
P2 = 40

As V is directly proportional to T

\[V \alpha T => V1 = k.T1 => \frac{ V1 }{ T1 } = k ------- 1\]
\[V \alpha T => V2 = k.T2 => \frac{ V2 }{ T2 } = k ------- 2\]
From 1 and 2

\[\frac{V1}{T1} = \frac{V2}{T2}--- 5\]

As V is inversely proportional to P

\[V \alpha \frac{ 1 }{ P } => V1 = k .\frac{ 1 }{ P1 } => k = V1.P1-------- 3\]
\[V \alpha \frac{ 1 }{ P } => V2 = k .\frac{ 1 }{ P2 } => k = V2.P2-------- 4\]
From 3 and 4

\[V1.P1 = V2.P2 --- 6\]

Insert the values in equations 5 and 6.
And you'll get V2.

Understood this? :)

Answer 2

The expression which correctly conveys the information that Volume is directly proportional to Temperature and inversely proportional to Pressure can be written as:
V = k*T/P ..........eqn (i) -> k is a constant here
If you see equation (i) and substitute higher values of T in it the volume will increase. If you substitute higher values of pressure on the other hand - volume will reduce.
Now if I want to eliminate k from the equation, I can also write:
V1 = k*T1/P1
and V2 = k*T2/P2
Divide the above equations and you get V1/V2 = T1P2/T2P1
Now you have some values of V1, T1, P1, T2 and P2. So I guess you can find V2 on your own

Answer 3

P1V1/T1=P2V2/T2

Answer 4

Thanks everyone for your support.

Answer 5

My bad you were right @Atlas :)

Answer 6

Never mind that it happens @AkashdeepDeb