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When The Tds Is Applied?

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amber Jhon answered
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).

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