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zorro
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Homework Statement
A vessel of volume Vo contains an ideal gas at pressure Po and temperature T. Gas is continuosly pumped out of this vessel at a constant volume rate dV/dt=r keeping the temperature constant. The pressure of the gas being taken out equals the pressure inside the vessel. Find the pressure of the gas as a function of time.
The Attempt at a Solution
http://latex.codecogs.com/gif.latex?\int_{V_{o}}^{V}dV&space;=&space;\int_{0}^{t}-rdt\\V-V_{o}=-rt\PV=nRT\\\frac{\partial&space;V}{\partial&space;t}P+\frac{\partial&space;P}{\partial&space;t}V=0\\\--rP+\frac{\partial&space;P}{\partial&space;t}%28V_{o}-rt%29=0\\\frac{dP}{P}=\frac{rdt}{V_{o}-rt}\\&space;P=\frac{P_{o}}{rt-V_{o}}\\Correct\answer\P=P_{o}e^{-\frac{rt}{V_{o}}}
Any help appreciated.