PV=nRT

[adrakdavra]

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Why is V and T slope is a straight line , where as P and V in curved line . I know that P and V are inversely related, but why their slope is curved ?

 

[Postictal Raiden]

Why is V and T slope is a straight line , where as P and V in curved line . I know that P and V are inversely related, but why their slope is curved ?

The graph for inversely related relationship is a downward curved line. However, the graph for something that is negatively related to something is a straight line with a negative slope. Confusing the two is a common mistake among many people, including me.

 

[dsoz]

Why is V and T slope is a straight line , where as P and V in curved line . I know that P and V are inversely related, but why their slope is curved ?

V and P are inversely related. The line starts in the upper left, and produces a curve to the lower right (almost shaped like a J, but no upward trend at the end). But if you take the reciprocal of one of them (1/P or 1/V), then plot the graph, it will end up being a straight line with positive slope that is related to the constant K.

Think about it this way. If you put more pressure on a gas, it will compress. At the beginning of this process it is easy (steep negative slope on the graph). But as you keep putting more and more pressure, it becomes more and more difficult to push it even more. Eventually it will take a HUGE amount of pressure to push down on the gas, even a little bit (very shallow negative slope on the graph, approaching the horizontal slope of zero).

On the other hand, V and T have a direct relationship (if T is measured in Kelvin). So the line would start at the origin (0,0) and progress up and to the right with a slope that is related to the constant K. As long as you keep increasing the kinetic energy of the molecules (the Kelvin temperature is a good approximation of the average kinetic energy of the molecules) they will continue to move faster and the volume will keep increasing.

Now in reality, increasing the temperature will eventually lead to the molecules breaking down into atoms, and atoms breaking down into charged particles (plasma), and this will impact the volume that is being measured as well.

dsoz

 

[adrakdavra]

The only I can think of is a non linear relationship between P and V. Now if we double pressure, does volume decrease by half or no??

 

[Postictal Raiden]

The only I can think of is a non linear relationship between P and V. Now if we double pressure, does volume decrease by half or no??

to answer this, u need to use the combined gas law. Increasing the pressure will lead to decrease in volume accordingly, but this relationship will eventually cease as the volume of the molecules will need to be considered. You can't squeeze molecules indefinitely, because under high pressure, gas molecules deviate from being ideal.

 

[adrakdavra]

so under an ideal gas conditions , it is linear or not?

 

[adrakdavra]

Does that mean 1/X is always non linear , just like C=lamda X f, lamda = 1/f so it is an inverse relation with curved slop