Enthalpy is a measure of total energy in a thermodynamic system. The following t
ID: 3434894 • Letter: E
Question
Enthalpy is a measure of total energy in a thermodynamic system. The following table presents enthalpy measurements on 16 water based systems. Four measurements are made on each of four systems which differ by concentration of NaCl (table salt)
Concentration (%)
Enthalpy
5
1.62
1.60
1.62
1.66
10
2.69
2.66
2.72
2.73
20
3.56
3.45
3.65
3.52
30
3.35
3.18
3.40
3.06
c) What pairs of concentrations, if any, can you conclude to have differing enthalpies? Use alpha = 0.05.
Concentration (%)
Enthalpy
5
1.62
1.60
1.62
1.66
10
2.69
2.66
2.72
2.73
20
3.56
3.45
3.65
3.52
30
3.35
3.18
3.40
3.06
Explanation / Answer
In the previous question related to same I have performed wrong calculations for ANOVA:
To test the hypothesis:
H0: Enthalpy is same for all concentration.
against
H1: Enthalpy differes for atleast one concentration.
ANOVA result is
One-way ANOVA: A1, B2, C1, D1
Source DF SS MS F P
Factor 3 7.451 2.484 15.66 0.000
Error 12 1.903 0.159
Total 15 9.354
S = 0.3982 R-Sq = 79.65% R-Sq(adj) = 74.57%
Individual 95% CIs For Mean Based on
Pooled StDev
Level N Mean StDev ---+---------+---------+---------+------
A1 4 1.6250 0.0252 (-----*-----)
B2 4 2.7000 0.0316 (------*-----)
C1 4 3.5450 0.0835 (------*-----)
D1 4 2.7425 0.7910 (-----*-----)
---+---------+---------+---------+------
1.40 2.10 2.80 3.50
Pooled StDev = 0.3982
This is MINITAb solution for ANOVA. AS p-value = 0< 0.05 we will reject the null hypothesis and conclude that enthalpy differes for atleast one concentration.
Now to test for for which pair of concentration have different enthalpy
All Pairwise Comparisons
A1 subtracted from:
Lower Center Upper -----+---------+---------+---------+----
B2 0.4615 1.0750 1.6885 (-----*-----)
C1 1.3065 1.9200 2.5335 (-----*-----)
D1 0.5040 1.1175 1.7310 (-----*-----)
-----+---------+---------+---------+----
-1.0 0.0 1.0 2.0
In this case 5% (A1) is compared with 10%(B2), 20%(c1) and 30% (D1) as comparison conclusion are as follows:
As CI of difference between 5% and10 % concentration does not include 0 this implies that there is significant difference between enthalphy level for 5% and 10%.
CI of difference between 5% and 20 % concentration does not include 0 this implies that there is significant difference between enthalphy level for 5% and 20%.
CI of difference between 5% and 30% concentration does not include 0 this implies that there is significant difference between enthalphy level for 5% and 30%.
B2 subtracted from:
Lower Center Upper -----+---------+---------+---------+----
C1 0.2315 0.8450 1.4585 (-----*------)
D1 -0.5710 0.0425 0.6560 (-----*------)
-----+---------+---------+---------+----
-1.0 0.0 1.0 2.0
As CI of difference between 10% and 20 % concentration does not include 0 this implies that there is significant difference between enthalphy level for 10% and 20%.
CI of difference between 10% and 30% concentration does not include 0 this implies that there is significant difference between enthalphy level for 10% and 30%.
C1 subtracted from:
Lower Center Upper -----+---------+---------+---------+----
D1 -1.4160 -0.8025 -0.1890 (-----*-----)
-----+---------+---------+---------+----
-1.0 0.0 1.0 2.0
CI of difference between 20% and 30% concentration include 0 this implies that there is no significant difference between enthalphy level for 20% and 30%.
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