dU =T dS – P dVRe-arrange the thermodynamic identity by solving for dS.Assume we are applying this new expression to an idealgas, re-write the du term in terms of the appropriate heatcapacity and temperature.Re-write the coefficient of the dV term in terms of volume.Connect these “classical" expressions for entropy to the"modern" interpretation where we are concerned with theuncertainty associated with position and momentum of theparticles in an ideal gas. Answer with sentences.Now, re-write the expression in terms of enthalpy so youcan connect entropy with enthalpy. Expalin why this finalexpression makes sense.

Given: The thermodynamic identity is dU=TdS-PdV. Introduction: Entropy, the measure of a system's thermal energy per unit temperature that is unavailable for doing useful work. Because work is obtained from ordered molecular motion, the amount of entropy is also a measure of the molecular disorder, or randomness, of a system. When a process occurs at constant pressure, the heat evolved (either released or absorbed) is equal to the change in enthalpy.Calculation: Evaluate the expression of dS rearranging the above identity. dU=TdS-PdVTdS=dU+PdVdS=1TdU+PdV Substitute cvdT for dU in the above expression where cv is the heat capacity. dS=1TcvdT+PdV Substitute nRTVfor P in the above expression. dS=1TcvdT+nRTVdV Write the relation between the entropy and enthalpy. ∆S=∆HT Here, H is the enthalpy and T is the temperature. This relation holds when the change in the Gibbs energy is zero. The modern entropy can be calculated for any probability distribution while the thermodynamic entropy refers to thermodynamic probabilities.

Answered: dU =T dS – P dV Re-arrange the…