Chapter3, Lesson C - Enthalpy Change of N2 Using the IG Heat Capacity

3C-4 :	Enthalpy Change of N2 Using the IG Heat Capacity							5 pts

Determine the enthalpy change and internal energy change of nitrogen in kJ/kg, as it is heated from 600 to 1000 K, using:

a.)	the Shomate Equation
b.)	the Cp value at the average temperature, 800 K
c.)	the Cp value at room temperature, 25°C

Read :	The Shomate Equation will yield the most accurate estimate of the enthalpy change. Assuming a constant value of Cp determined at the average temperature should yield a reasonable estimate of ΔH as well. Using the Cp value at room temperature should not be very accurate. We can compare this result to the value we get in part (a).




Given :	T1	600	K	T2	1000	K

Find :	ΔH1-2 =	???	kJ/kg

Assumption:		a.)	Nitrogen behaves as an ideal gas
		b.)	Nitrogen behaves as an ideal gas with a linear relationship between Cp and T.
			This is equivalent to using a constant value of Cp that is equal to the average of Cp(T1) and Cp(T2).

		c.)	Nitrogen behaves as an ideal gas with a constant heat capacity.

Solution :	Let's begin by collecting the data we will need from the NIST Webbook :

					Temp (K)	298 - 6000
	MW	28.01	g/mole		A	26.092
					B	8.218801
					C	-1.976141
					D	0.159274
					E	0.044434

Part a.)	The enthalpy change associated with a temperature change for an ideal gas can be determined from :
								Eqn 1

	The Shomate Equation for the ideal gas heat capacity is :							Eqn 2

				where :				Eqn 3

				and :				Eqn 4

	Combining Eqns 1, 2 and 3 and integrating yields :


								Eqn 5

	Plug in values for the temperatures and the constants to get :					ΔH	12615	J/mol

								Eqn 6

Answer :						ΔH	450.4	kJ/kg

	We can determine ΔU using the definition of enthalpy :							Eqn 7

	For ideal gases, Eqn 7 becomes :							Eqn 8

	We can then solve Eqn 8 for ΔU :							Eqn 9

	R	8.314	J/mol-K			ΔU	9289	J/mol

								Eqn 10

Answer :						ΔU	331.6	kJ/kg

Part b.)	First we need to use the Shomate Equation, Eqns 2 & 3, to evaluate Cp(T1) and Cp(T2) :

	t1	0.6				Cp(T1)	30.470	J/mol-K
	t2	1				Cp(T2)	32.538	J/mol-K

	Therefore, the average value of Cp is :					Cpavg	31.504	J/mol-K

	When the heat capacity is a constant, Eqn 1 simplifies to :							Eqn 11

						ΔH	12602	J/mol

Answer :						ΔH	449.9	kJ/kg

	This amounts to about 0.1% error relative to the result in part (a).					ΔU	331.2	kJ/kg

Part c.)	We can use Eqns 2 & 3 to evaluate the heat capacity at 25°C or 298.15 K :

	t1	0.29815			Cp(298.15K)		28.871	J/mol-K

						ΔH	11548	J/mol

Answer :						ΔH	412.3	kJ/kg

	This amounts to almost 9% error relative to the result in part (a).					ΔU	293.6	kJ/kg
	That is not acceptable.

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