The relationship between pressure and the den | vedclass

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(C) The relationship is given by $P = K\rho$.From the ideal gas law,we know that $PV = nRT = \frac{m}{M_0} RT$,where $m$ is the mass and $M_0$ is the

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Only if the temperature is kept constant

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(C) The relationship is given by $P = K\rho$.From the ideal gas law,we know that $PV = nRT = \frac{m}{M_0} RT$,where $m$ is the mass and $M_0$ is the molar mass.Rearranging for density $\rho = \frac{m}{V}$,we get $P = \frac{\rho RT}{M_0}$.Comparing this with $P = K\rho$,we identify $K = \frac{RT}{M_0}$.Since $R$ is the universal gas constant and $M_0$ is the molar mass of the gas,$K$ remains constant only if the temperature $T$ is kept constant.Therefore,Boyle's law holds true only if the temperature is constant.

The relationship between pressure and the density of a gas expressed by Boyle's law,$P = K\rho$,holds true:

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