The work done in compressing air from state 1 (at the beginning of compression stroke) to state 2 (end of compression) by a piston-cylinder type compressor without clearance volume with standard terminologies is:

1
\(\frac{n}{(n\;-\;1)}P_2V_2\left\{\left(\frac{P_2}{P_1}\right)^{\frac{n\;-\;1}{n}}-1\right\}\)
2
\(\frac{n(P_2V_2\;-\;P_1V_1)}{n\;-\;1}\)
3
\(\frac{n}{(n\;-\;1)}P_1V_1\left\{\left(\frac{P_2}{P_1}\right)^{\frac{n\;-\;1}{n}}-1\right\} \)
4
\(mRC_p(T_2\;-\;T_1)\)

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