dh = Tds + vdP differentiating with respect to temp. that is dh / dT dh / dT = ds + (vdP / dT) using PV= nRT P= nRT/V dp/dT = nR/V so collective term (vdP / dT) = nR dU = T dS - p dV from above dS = (dU+pdV) / T putting these values in dh / dT = ds + (vdP / dT) dh / dT =[ (dU+pdV) / T ] + nR now dU= Cv dT and pdV = nRdT so (dU+pdV) = Cv dT + nRdT and (dU+pdV) / T = [Cv dT + nRdT ] / T now using Cv = Cp - R we will get (dU+pdV) / T = [(Cp - R)dT + nRdT ] / T so dh / dT =[ (dU+pdV) / T ] + nR = {[(Cp - R)dT + nRdT ] / T } + nR Solution dh = Tds + vdP differentiating with respect to temp. that is dh / dT dh / dT = ds + (vdP / dT) using PV= nRT P= nRT/V dp/dT = nR/V so collective term (vdP / dT) = nR dU = T dS - p dV from above dS = (dU+pdV) / T putting these values in dh / dT = ds + (vdP / dT) dh / dT =[ (dU+pdV) / T ] + nR now dU= Cv dT and pdV = nRdT so (dU+pdV) = Cv dT + nRdT and (dU+pdV) / T = [Cv dT + nRdT ] / T now using Cv = Cp - R we will get (dU+pdV) / T = [(Cp - R)dT + nRdT ] / T so dh / dT =[ (dU+pdV) / T ] + nR = {[(Cp - R)dT + nRdT ] / T } + nR.