Relations for sound speed and ideal gas
Relations of sound speed and ideal gas are derived using the derivatives of thermodynamic properties.
Derivatives of thermodynamic properties:
- By definition .
- Let’s write it in terms of P, ρ, and u instead. Using equation above and letting x=P, w=ρ , z=s, and y=u, we have
- Using the relation we have
- For an ideal gas, P = ρRT . If the specific heats are constant, then we also have du = Cv dT . With these relations, we have