Tds equations are applied to develop a relationship between different thermodynamic variables such as temperature, volume, pressure and entropy. First tds equation is a connection between derivatives of entropy with respect to temperature and volume, when entropy is a function of temperature and volume. We can derive the second tsd equation by treating entropy as a function of temperture and pressure. It is a relationship between the derivatives of entropy with respect to temperature and pressure. Third tds equation connects pressure and volume. Consider S, T, P and V as the entropy, temperature, pressure and volume of a gas respectively, then tds equations are;
TdS= CvdT + T (dP/dT)v dV (first tds equation)
TdS= CpdT - T (dV/dT)p dP (second tsd equation)
TdS= Cv (dV/dP)T (dT/dV)p dP + Cp (dt/dV)p dV (third tds equation).
TdS= CvdT + T (dP/dT)v dV (first tds equation)
TdS= CpdT - T (dV/dT)p dP (second tsd equation)
TdS= Cv (dV/dP)T (dT/dV)p dP + Cp (dt/dV)p dV (third tds equation).