Enthalpy is a measure of total energy in a thermodynamic sys

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

b) Is it plausible that the enthalpy is the same at all concentrations? Explain.

Solution

We can perform one way analysis of variance (ANOVA) to test the null hypothesis:

Ho: Enthalpy is the same at all the concentration.

against

H1: Enthalpy of atleast one concentration differes significantly .

ANOVA result

One-way ANOVA: A, B, C, D

Source DF     SS     MS     F      P
Factor   3 0.040 0.013 0.02 0.996
Error   12 8.637 0.720
Total   15 8.676

S = 0.8484   R-Sq = 0.46%   R-Sq(adj) = 0.00%

                          Individual 95% CIs For Mean Based on
                          Pooled StDev
Level N    Mean   StDev ----+---------+---------+---------+-----
A      4 2.8050 0.8726    (-----------------*------------------)
B1     4 2.7225 0.8170 (-----------------*------------------)
C      4 2.8475 0.9078    (------------------*-----------------)
D      4 2.7425 0.7910 (------------------*-----------------)
                          ----+---------+---------+---------+-----
                            2.00      2.50      3.00      3.50

Pooled StDev = 0.8484
This is one way ANOVA result using Minitab as P-value = 0.996 > 0.05 we fail to reject the null hypothesis and hence conclude that enthalpy is same at all concentration and it is not affected by NaCl.

Manually this can done by performing ANOVA and comparing cal F-value with tab. F_3,12,0.025 and we can reject the null hypothesis if 0.02 > tab. F_3,12,0.025