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This equation describes an ideal gas, which is essentially a simplified model of real gases to help us in calculations. Since there are 4 unknown's in this equation, we can use this equation when we have three givens, which then can be used to calculate the final unknown.
First of all, this equation can only be used on ideal gas. 1) The volume of gas particles are really small, which can be neglected 2) Gas particles are always moving around randomly in the system 3) There are no interactions between the particles 4) The collisions between gas particles and the wall of the system are elastic that does not cost any energy. We can use this equation to calculate any one variable in it if we know the others. Also, we can use this equation to learn the relationships among temperature, pressure, and amount of substance. The difference between these two equations is that the second one is normally used under the situation that gas does work on the environment. The reason is, only if the gas does work, the volume can change, which causes the change of temperature in turn. Hope this helps!
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