Opening the book…
Important Equations
| Kinetic Energy |
\[E_{k} = \frac{1}{2} mu^{2}\] \[\dot{E}_{k} = \frac{1}{2} \dot{m} u^{2}\] |
|
| Potential Energy |
\[E_{p} = m g z\] \[\dot{E}_{p} = \dot{m} g z\] |
\(\Delta U + \Delta E_{k} + \Delta E_{p} = Q + W\) |
| Flow Work | \(\dot{W}_{fl} = \dot{W}_{fl-in} - \dot{W}_{fl-out} = P_{in}\dot{V}_{in} - P_{out}\dot{V}_{out}\) | |
| Steady-state Open System Energy Balance |
\[\dot{Q} + \dot{W} = \Sigma_{out} \dot{E}_{j} - \Sigma_{in} \dot{E}_{j}\] \[\dot{Q} + \dot{W}_{s} = \Delta\dot{H} + \Delta\dot{E}_{k} + \Delta\dot{E}_{p}\] |
|
| Enthalpy |
\[\hat{H} = \hat{U} + P\hat{V}\] \[\Delta\hat{H} = \Sigma_{i}\Delta\hat{H}_{i}\] |
|
| Heat Capacity (closed system) | \(C_{V}(T) = \bigg(\frac{\delta\hat{U}}{\delta T}\bigg)_{V}\) | |
| Internal Energy (closed system) | \(d\hat{U} = C_{V}(T)dT\)
\[\Delta\hat{U} = \int^{T_{2}}_{T_{1}}C_{V}dT\] |
|
| Heat Capacity (open system) | \(C_{P}(T) = \bigg(\frac{\delta\hat{H}}{\delta T}\bigg)_{P}\) | |
| Enthalpy (open system) | \(\Delta\hat{H} = \int^{T_{2}}_{T_{1}}C_{P}dT\) | |
| Heat of Reaction Method | \(\Delta\dot{H} = \xi\Delta\dot{H}_{r} + \Sigma\dot{n}_{out}*\int^{T_{out}}_{T_{ref}}C_{P}dT - \Sigma\dot{n}_{in}*\int^{T_{in}}_{T_{ref}}C_{P}dT\) | |
| Heat of Formation Method | \(\xi\Delta\dot{H}^{\circ}_{r} = \Sigma\dot{n}_{out}*\hat{H}^{\circ}_{f,i} - \Sigma\dot{n}_{in}*\hat{H}^{\circ}_{f,i}\) |
Terms to Know
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