i dont know where to begin when solving this problem???

Question

Boyles Law: The volume V of a givenmass of a gas varies directly as the temperature T and inversely as the pressure, P. If V=231cm^3 when T=42° and P=20Kg/cm^2, what is the volume when T=30° and P=15kg/cm^2? round to the nearest whole cm^3

Answer 1

First, the reference to Boyles' Law is not important (and may not even be correct; see -- Combined gas law is the combination of Charles's law, Boyle's law, and Gay-Lussac's law); those formulas use temperature (T) in degrees Kelvin and this problem doesn't even specify whether 42 and 30 are degrees Fahrenheit, Celsius or Kelvin (although the problem probably misuses the formulas by specifying the wrong ranges) --

  this is meant to be an algebra problem.

 

The keywords are "directly" and "inversely" and they both relate to "proportional."

 

To vary directly with the Temperature (T), the Volume (V) must follow an equation that looks like:

                           V = k₁T + k₂         where k₁ and k₂ are some constants;  so, as T goes up, V will go up

    This makes sense; heating expands the gas.

 

To vary inversely with the Pressure (P), the Volume (V) must follow an equation that looks like:

                          V = k₃/P + k₄          where k₃ and k₄ are some constants;  so, as P goes up, V will go down

    This also makes sense; compressing the gas reduces the volume it takes.

 

Putting these into one formula (which the problem should have given you to start with):

                         V = kT/P   

   (note:  we are neither good chemists, physicists, engineers, or ... because we are now disregarding constants)

 

The problem gives:       V=kT/P

                                 231 = k(42)/20

   and asks for V:            V = k(30)/15

(note again:  my best guess is that they don't expect you to convert to Kelvin)

 

So, since their k is some constant, we may set the equations equal:

              k = 15V/30 = (20)(231)/42   and solve for V

                       V = (2)(20)(231)/42        (multiply both sides by 2)

                         V = 220 cm^3

 

Now, it also seems suspicious to me that the volume is a whole number and does not need to be "rounded to the nearest whole cm^3."  This often happens when the author of the problem works it backwards to make the computations easy (isn't 231 cm^3 an unusual number for a volume?).