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 CCBYNCND4.0 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 nonideal mixtures. Typical units are per mole of solute, not solution. 
For a particular firefighting 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 Nm/sec = watts
print("fire pump requirement [watts] =", P)
print("fire pump requirement [hp] =", P/746)
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?