The pressure gauge on a cylinder of gas registers the gauge pressure, which is t

Question

The pressure gauge on a cylinder of gas registers the gauge pressure, which is the difference between the interior and exterior pressure, P_0. When the cylinder is full, the mass of the gas in it is m, at a gauge pressure of P_i. Assuming the temperature of the cylinder remains constant, use the ideal gas law and a relationship between moles and mass to show that the mass of the gas remaining in the cylinder when the gauge pressure reading P_f is given by the equation below. m_f=m_i(P_f+P_0/P_i+P_0)

Explanation / Answer

we know that

PV = m/M RT

here R T M and V are constants

therefore

P2/P1 = m2/m1

P1 = Pi + P0

P2 = Pf + P0

m2 = mf

m1 = mi

mf/mi = Pf+P0/Pi+P0

mf = mi ( Pf+P0 / Pi+P0)

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