Constant Pressure Pathway
- Most laboratory-based chemistry occurs at constant pressure
- It is convenient to define a new thermodynamic quantity called
enthalpy
\[H\equiv U+PV\] \[dH \equiv dU+d(PV) = dU+PdV+VdP\] \[dH=dq+dw+PdV+VdP\]
- If only \(PV\) work can be done
then \[dH=dq-PdV+PdV+VdP=dq+VdP\]
\[dH=dq-PdV+PdV+VdP=dq+VdP\]
- For reversible changes (constant pressure), \(dP=0\), so
\[dH=dq\]
- This means that for a constant pressure situation, the change in
heat equals the change in enthalpy
- By the way, this is why the symbol for enthalpy is an “\(H\)” … it originally stood for HEAT
Example 3.5
Consider \(1.00mol\) of an ideal gas
with \(C_P=\frac{5}{2}\) that changes
from temperature from \(125K\) to \(255K\) at a constant pressure of \(10.0atm\). Calculate \(\Delta U\), \(\Delta H\), \(q\), and \(w\) for this change.
Example 3.6
Calculate \(q\), \(w\), \(\Delta
U\), and \(\Delta H\) for \(1.00mol\) of an ideal gas expanding
reversibly and isothermally at \(273K\)
from a volume of \(22.4L\) and a
pressure of \(1.00atm\) to a volume of
\(44.8L\) and a pressure of \(0.500atm\).
Putting the First Law to Work