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• Notes
• Clausius inequality : the cyclic integral of $\delta Q / T$ is always less than or equal to zero

$\oint \frac{\delta Q}{T} \leq 0$

• Kelvin–Planck statement of the second law: no system can produce a net amount of work while operating in a cycle and exchanging heat with a single thermal energy reservoir
• Entropy is an extensive property of a system

$d S=\left(\frac{\delta Q}{T}\right)_{\mathrm{int} \mathrm{rev}} \quad(\mathrm{kJ} / \mathrm{K})$

• The entropy change of a system during a process can be determined by

$\Delta S=S_{2}-S_{1}=\int_{1}^{2}\left(\frac{\delta Q}{T}\right)_{\mathrm{int,rev}} \quad(\mathrm{kJ} / \mathrm{K})$

• Internally reversible, isothermal heat transfer processes:

$\Delta S=\int_{1}^{2}\left(\frac{\delta Q}{T}\right)_{\mathrm{intrev}}=\int_{1}^{2}\left(\frac{\delta Q}{T_{0}}\right)_{\mathrm{intrev}}=\frac{1}{T_{0}} \int_{1}^{2}(\delta Q)_{\mathrm{int} \text { rev }}$

$\Delta S=\frac{Q}{T_{0}} \quad(\mathrm{k} J / \mathrm{K})$

where $T_{0}$ is the constant temperature of the system and $Q$ is the heat transferfor the internally reversible process