A gas is considered thermally perfect when its internal energy and enthalpy are functions of temperature alone. This means that in a thermally perfect gas, both the internal energy (\(U\)) and the enthalpy (\(H\)) only change with respect to temperature (\(T\)), rather than pressure (\(p\)) or volume (\(V\)).
Mathematically, this can be represented as:
\(U = f(T)\)
\(H = g(T)\)
where \(f\) and \(g\) are functions entirely dependent on the temperature. This characteristic is significant in thermodynamics, especially when dealing with ideal gases, where specific heats (\(c_v\) and \(c_p\)) are also functions of temperature, implying that:
\(c_v = c_v(T)\)
\(c_p = c_p(T)\)
Thus, a thermally perfect gas behaves predictably because its properties are functions of one variable, simplifying the analysis in aerospace engineering applications.