# Science geniuses please? Or anyone who can explain?

For a test tomorrow I am supposed to know three laws of mechanical efficiency, and those are Pascal's law, Boyle's law, and Charles's law. I understand Pascal's law, F= (P) (A), P= F/A, and A= F/P but I am having a lot of trouble with the other two. I do not understand it at all and my teacher could not explain it either. Here are the other 2 laws:

Boyle's Law: This law states that the volume of a given mass of gas at a constant temperature is inversely proportional to its pressure: (P) x (V)= T (constant temperature).

Example: If temperature is not changed, what happens to volume if the pressure is increased?

Initial pressure and volume= Final pressure and volume

Initial P1= 10 kPa (kilo pascals)

Initial V1= 10 m3

Final P2= 20 kPa

Final V2= ?

(P1) X (V1)= (P2) X (V2)

(10 kPa) x (10 m3)= (20 kPa) x (V2)

(100 kPa m3) = V2

___________

(20 kPa)

Final volume: 5 m3 = V2 (V squared)

Charles' Law: This law states that the volume of a fixed mass of gas at a constant pressure is directly proportional to its temperature (in Kelvins): V/T= P (constant pressure)

Example:

If pressure is not changed, what happens to volume if the temperature (in Kelvins) is increased?

Initial temperature and volume= Final temperature and volume

Initial V1= 10 m3 (cubed)

Initial T1= 273 K

Final V2= ?

Final T2= 373 K

(V1)= (V2)

____ ____

(T1) (T2)

(10 m3)= (V2)

______ _____

(273 K) (373 K)

Final volume: 13.7 K

Relevance

Hi,

Those 2 equations are pretty much the same thing. Here is the simple idea below- even if you don't 100% understand, learn how to do it. Understanding will often come later.

1st law says simply, as long as temp is held constant:

P1*V1 = P2*V2

Where P1 is pressure 1, V1 is pressure 1, P2 is pressure 2, and V2 is pressure 2. Make sure that the variables with "1" in them pertain to the same state (initial) of gas, and the variables with "2" in them pertain to the other state (final) of gas. What I mean is, if initially the sample has P = 15 Pa and V=5 m^3, then make P1 = 15 and V1 = 5. Do not make P1=15 and V2=5, because "1" and "2" are the gas at different times. It's easier to remember like this, I think:

P_initial*V_initial = P_final*V_final

So the deal with this question is you'll be given 3 of those variables, and you solve for the 4th. You will always be given 3 out of 4, or the question is not solvable for a single value. No problem.

The 2nd law, Charles' Law, is really from the same exact equation, just rearranged. So instead of P1*V1=P2*V2, now you have V1/T1 = V2/T2.

Rewrite as

V_initial/T_initial = V_final/T_final

Same exact procedure.

As to why these are true, well first of all they both come from the ideal gas law, but otherwise, there's probably some thermodynamics explanation in there. Don't worry about that for the moment- just figure out how to do the problems.

Hope this helps.