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## Homework Statement

This question is to due with a compressor experiment. I've actually posted 2/3 questions on this write up in the past 2 days. Anyway, a compressor takes air from the atmosphere and compresses it before forcing it into a receiver volume. You are asked to calculate the mass of air that is initially in the receiver, the final mass in the receiver and subsequently the mass that has been transferred in. You are given the atmospheric conditions P

_{0}and T

_{0}as well as the final conditions P

_{F}and T

_{F}. The volume of the receiver is also given. Also n, the polytropic exponent was found to be ≈ 1 (1.014 to be exact). Finally, you are asked to find the volume that the transferred mass of gas occupies at atmospheric conditions using P

_{1}V

_{1}

^{n}= P

_{2}V

_{2}

^{n}= PV

^{n}

## Homework Equations

Given equations:

P

_{1}V

_{1}

^{n}= P

_{2}V

_{2}

^{n}= PV

^{n}

PV = mRT.

## The Attempt at a Solution

PV = mRT.

m = PV/RT.

m

_{initial}= P

_{0}V/RT

_{0}.

m

_{final}= P

_{F}V/RT

_{F}.

m

_{transferred}= m

_{final}- m

_{initial}.

Correct so far?

This is where I get a little stuck. You are told to use P

_{1}V

_{1}

^{n}= P

_{2}V

_{2}

^{n}= PV

^{n}to calculate the volume that m

_{transferred}will occupy at P

_{0}and T

_{0}. Why is it not ok to use PV = mRT for this question? Subbing m

_{transferred}, P

_{0}and T

_{0}into the ideal gas law and solving for V. I've actually asked the lecturer why this is and he told me that the ideal gas law could be used but it's use will be a little more involved. Anybody have any ideas where I may be going wrong? And how I could actually use P

_{1}V

_{1}

^{n}= P

_{2}V

_{2}

^{n}= PV

^{n}to solve for the volume occupied at atmospheric temp and pressure?