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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

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dh = Tds + vdPdifferentiating with respect to temp. that is dh d.pdf

  • 1. 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
  • 2. (dU+pdV) / T = [(Cp - R)dT + nRdT ] / T so dh / dT =[ (dU+pdV) / T ] + nR = {[(Cp - R)dT + nRdT ] / T } + nR