Are enthalpy and entropy affected by temperature?

1 Answer
Truong-Son N.
Dec 13, 2015

Yes, they are. Here is how:

#DeltabarS = int_(T_1)^(T_2) (barC_P)/T dT#

#DeltabarH = int_(T_1)^(T_2) barC_P dT#

where #barC_P# is the molar heat capacity in a constant pressure system, and #DeltaS# and #DeltaH# are the change in entropy and enthalpy, respectively.

So, let's say you had water, whose chemistry molar heat capacity is defined as #"75.375 J/mol"*"K"#. Then, we have, from #273# to #"298 K"#:

#DeltabarS = int_("273 K")^("298 K") (barC_P)/T dT#

#= barC_P|[ln|T_2| - ln|T_1|]|_("273 K")^("298 K")#

#= 75.375*(ln(298) - ln(273))#

#color(blue)("= 6.604 J/mol"*"K")#

#DeltabarH = int_("273 K")^("298 K") barC_P dT#

#= barC_P(T_2 - T_1)#

#= 75.375(298 - 273)#

#color(blue)("= 1884.38 J/mol")#

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