Freakin out on this question. Need help

Question

The volume V of a fixed amount of a gas varies directly as the temperature T and inversely as the pressure P.

Suppose that V=120 cm^3 when T=260 Kelvin and P=13^kg/2/cm. Find the pressure when T=380 Kelvin and V=152cm^3.

 

My head is spinning

Answer 1

Directly proportional means that both variables act the same way.  Inverse proportional means that both variables act in the opposite way.

 

The equation you should end up with is

 

V = KT/P

 

where:

V = volume

K = constant

T = temperature

P = pressure

 

You need to first solve for K using the values: T=260 , P=13, and V=120

 

K = VP / T

K = (120)(13) / 260

K = 6

 

Now your equation is

 

V = 6T/P

 

Solve for P when  T=380 and V=152.

Answer 2

Based on the question, it seems like this is 2 parts. First you need to use the given information to make a formula for Volume in terms of Temp. and Pressure. Varies directly means that when V increases, T increases, and therefore T will be in the numerator. Varies inversely means when V increases, P decreases, or when P increases, V decreases. Therefore P must be in the denominator. Something like this:

 

V = T/P

However, 120 does not equal 260/13. So that means there must be a constant in our equation, and we can solve for it since it's the only unknown:

 

V = constant * (T/P)

120 = c*(260/13)

c = 6

 

That means this is our formula:

V = 6*(T/P)

 

And we can substitute 152, and 380 into the formula and solve for P:

152 = 6*(380/P)

P = 6*380/152 = 15

 

Hopefully that was the correct approach. Good luck!