What is the significance of deriving PV=K?

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The discussion focuses on the physical significance of deriving the equation PV=K, particularly through the volume derivative. The derivative illustrates the relationship between pressure and volume changes, highlighting gas elasticity. It emphasizes that this derivation is relevant to the ideal gas law, where temperature remains constant, affecting internal energy. The reference to Bernoulli suggests a connection to hydrodynamics, though the primary focus remains on gas behavior. Understanding this derivation is crucial for grasping gas properties under constant temperature conditions.
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Hi, I'm wondering what the physical meaning there is to taking the volume derivative of the equation pv=k.

d/dv [ pv = k ]
(v * dp/dv ) + p = 0

I know this has to do with the elasticity of a gas but I am unsure as to why this process of deriving the equation pv = k was taken. Any help would be appreciated.

Thanks
 
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The equation is important because in this process...according to the ideal gas equation,the temperature remains constant...and thus the internal energy.
I hope this is what you asked...if not please elaborate a little more on what you mean...
 

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