This notebook contains course material from CBE20255 by Jeffrey Kantor (jeff at nd.edu); the content is available on Github. The text is released under the CC-BY-NC-ND-4.0 license, and code is released under the MIT license.
Internal energy ($U$) and enthalpy ($H = U + PV$) are thermodynamic state variables. We can use this property to compute changes in internal energy or enthalpy due to changes in pressure, temperature, phase, composition, and mixing/solution. The following table presents basic formulas for these calculations.
Change in | $\Delta\hat{H}=\Delta\hat{U} + P\Delta\hat{V}$ | $\Delta\hat{U}$ | Comments |
---|---|---|---|
Pressure | ~ 0 (gas) ~$\hat{V}\Delta P$ (solid or liquid) |
~ 0 | Generally neglected except for large pressure changes. |
Temperature | $\int_{T_1}^{T_2} C_p(T) dT$ $\approx \bar{C}_p(T_2 - T_1)$ |
$\int_{T_1}^{T_2} C_v(T)dT$ $\approx \bar{C}_v(T_2 - T_1)$ |
Expressions available for $C_p(T)$ $C_p \approx C_v + R$ (gases) $C_p \approx C_v$ (liquids and solids) |
Phase | $\Delta\hat{H}_{vap}$ (liquid to vapor) $\Delta\hat{H}_{m}$ (solid to liquid) |
$\Delta\hat{U}_{vap}\approx\Delta\hat{H}_{vap}-RT_b$ $\Delta\hat{U}_m\approx\Delta\hat{H}_m$ |
|
Composition due to Reaction |
$\Delta\hat{H}^\circ_r =\sum_i \nu_i \Delta\hat{H}^\circ_{f,i}$ $\Delta\hat{H}^\circ_r = -\sum_i \nu_i \Delta\hat{H}^\circ_{c,i}$ |
$\Delta\hat{U}_r \approx \Delta\hat{H}_r - RT \Delta n_r$ $\Delta\hat{U}_r \approx \Delta\hat{H}_r$ (solid or liquid) |
$\Delta n_r$ is the cange in moles due to reaction Standard conditions are 25$^\circ$C and 1 atm. Be sure all data uses same standard conditions. |
Composition due to Mixing/Sol'n |
$\Delta\hat{H}_{soln}$ $\Delta\hat{H}_{mix}$ |
$\Delta\hat{U}_{soln} \approx \Delta\hat{H}_{soln}$ $\Delta\hat{U}_{mix} \approx \Delta\hat{H}_{mix}$ |
Important for non-ideal mixtures. Typical units are per mole of solute, not solution. |
For a particular fire-fighting situation, it is determined that 1,250 gpm is required. The fire hydrant will supply sufficient water at a pressure of 35 psig. A pressure of 180 psig is needed to reach the top of the 212 foot bulding. What size engine (in Hp) is required to power the fire pump?
Vdot = 1250/264.172/60 # flow in m**3/s
dP = (180 - 35)*101325/14.696 # pressure change in pascals (N/m**2)
P = Vdot*dP # power in N-m/sec = watts
print("fire pump requirement [watts] =", P)
print("fire pump requirement [hp] =", P/746)
fire pump requirement [watts] = 78841.96681903958 fire pump requirement [hp] = 105.68628259924876
Solid phenol at 25°C and 1 atm is converted to phenol vapor at 300°C and 3 atm. How much heat will be required?