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• Notes

$w_{\mathrm{rev}}=-\int_{1}^{2} v d P-\Delta \mathrm{ke}-\Delta \mathrm{pe} \quad(\mathrm{kJ} / \mathrm{kg})$

When the changes in kinetic and potential energies are negligible, this equation reduces to

$w_{\mathrm{rev}}=-\int_{1}^{2} v d P$

• the reversible work output associated with an internally reversible process in a steady-flow device

$w_{\text { revin }}=\int_{1}^{2} v d P+\Delta k e+\Delta p e$

• the Bernoulli equation in fluid mechanics:

For the steady flow of a liquid through a device that involves no work interactions, the work term is zero

$v\left(P_{2}-P_{1}\right)+\frac{V_{2}^{2}-V_{1}^{2}}{2}+g\left(z_{2}-z_{1}\right)=0$

• minimizing the compressor work:
1. Approximate an internally reversible process as much as possible by minimizing the irreversibilities such as friction, turbulence, and nonquasi-equilibrium compression.
2. Keep the specific volume of the gas as smallas possible during the compression process.
• Isentropic$\left(P v^{k}=$ constant \right$) :$

$w_{\text { comp,in }}=\frac{k R\left(T_{2}-T_{1}\right)}{k-1}=\frac{k R T_{1}}{k-1}\left[\left(\frac{P_{2}}{P_{1}}\right)^{(k-1) / k}-1\right]$

• Polytropic$\left(P V^{n}=$ constant \right$) :$

$w_{\text { comp, in }}=\frac{n R\left(T_{2}-T_{1}\right)}{n-1}=\frac{n R T_{1}}{n-1}\left[\left(\frac{P_{2}}{P_{1}}\right)^{(n-1) / n}-1\right]$

• Isothermal$(P v=$ constant $) :$

$w_{\text { comp, in }}=R T \ln \frac{P_{2}}{P_{1}}$