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strokes required to obtain 1% of the original mass

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Problem #1

A vacuum pump removes 15% of the air that is in a container at the beginning of a stroke. If m_r is the mass of air in the container after the rth stroke:

(i) Express m_2 and m_3 in terms of the original mass m_0.
(ii) How many strokes are required to obtain 1% of the original mass?
(iii) Given that m_2 = 7.225 kg, determine

SUMMATION[r=0 to infinity] m_r

Problem #2

The pressure, p, and volume, V, of a gas undergoing a polytropic process are related by the equation
p1 (V1)^n = p2 (V2)^n
where n is the polytropic index.

If
p1 V1 / T1 = p2 V2 / T2
determine an expression for p1, in terms of p2, T1, T2 and n.

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Determine an expression for p1, in terms of p2, T1, T2 and n.

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