37 Energy Balances Review
Important Equations
| Kinetic Energy |
[latex]E_{k} = \frac{1}{2} mu^{2}[/latex] [latex]\dot{E}_{k} = \frac{1}{2} \dot{m} u^{2}[/latex] |
| Potential Energy |
[latex]E_{p} = m g z[/latex] [latex]\dot{E}_{p} = \dot{m} g z[/latex] [latex]\Delta E_{p} = E_{p2} - E_{p1} = m g (z_{2} - z_{1})[/latex] |
| First Law of Thermodynamics[latex][/latex] | [latex]\Delta U + \Delta E_{k} + \Delta E_{p} = Q + W[/latex] |
| Flow Work | [latex]\dot{W}_{fl} = \dot{W}_{fl-in} - \dot{W}_{fl-out} = P_{in}\dot{V}_{in} - P_{out}\dot{V}_{out}[/latex] |
| Steady-state Open System Energy Balance |
[latex]\dot{Q} + \dot{W} = \Sigma_{out} \dot{E}_{j} - \Sigma_{in} \dot{E}_{j}[/latex] [latex]\dot{Q} + \dot{W}_{s} = \Delta\dot{H} + \Delta\dot{E}_{k} + \Delta\dot{E}_{p}[/latex] |
| Enthalpy |
[latex]\hat{H} = \hat{U} + P\hat{V}[/latex] [latex]\Delta\hat{H} = \Sigma_{i}\Delta\hat{H}_{i}[/latex] |
| Heat Capacity (closed system) | [latex]C_{V}(T) = \bigg(\frac{\delta\hat{U}}{\delta T}\bigg)_{V}[/latex] |
| Internal Energy (closed system) | [latex]d\hat{U} = C_{V}(T)dT[/latex]
[latex]\Delta\hat{U} = \int^{T_{2}}_{T_{1}}C_{V}dT[/latex] |
| Heat Capacity (open system) | [latex]C_{P}(T) = \bigg(\frac{\delta\hat{H}}{\delta T}\bigg)_{P}[/latex] |
| Enthalpy (open system) | [latex]\Delta\hat{H} = \int^{T_{2}}_{T_{1}}C_{P}dT[/latex] |
| Heat of Reaction Method | [latex]\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[/latex] |
| Heat of Formation Method | [latex]\xi\Delta\dot{H}^{\circ}_{r} = \Sigma\dot{n}_{out}*\hat{H}^{\circ}_{f,i} - \Sigma\dot{n}_{in}*\hat{H}^{\circ}_{f,i}[/latex] |
Terms to Know
Feedback/Errata