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= C

TdS= C

TdS= C

TdS= C

_{v}dT + T (dP/dT)_{v}dV (first tds equation)TdS= C

_{p}dT - T (dV/dT)_{p}dP (second tsd equation)TdS= C

_{v}(dV/dP)_{T}(dT/dV)_{p}dP + C_{p}(dt/dV)_{p}dV (third tds equation).