As we learned in class, the specific heat capacity per molecule of a given subst

Question

As we learned in class, the specific heat capacity per molecule of a given substance is CV = f /2 kB, where f is the number of degrees of freedom, and has units of J/(K molecule). The specific heat capacity cV of a substance is defined to be the energy per unit mass per unit temperature, and often given in units of J/(K g). Answer the following questions concerning H2O: (a) When H2O is frozen (ice), it has a specific heat capacity of 2.05 J/(g K). How many degrees of freedom f does ice have? (b) When H2O is liquid (water), it has a specific heat capacity of 4.19 J/(g K). How many degrees of freedom f does water have? (c) When H2O is gas (steam), it has a specific heat capacity of 2.08 J/(g K). How many degrees of freedom f does steam have?

Explanation / Answer

molecular mass of H2O=18 grams

then mass per molecule=18/(6.023*10^23)=2.9885*10^(-23) grams

heat capacity per molecule=(f/2)*kB

==>2.9885*10^(-23)*2.05=(f/2)*1.38*10^(-23)

==>f=4.43

part b:

using the same method as above,

2.9885*10^(-23)*4.19=(f/2)*1.38*10^(-23)

==>f=9

part c:

using the same method as part a,

2.9885*10^(-23)*2.08=(f/2)1.38*10^(-23)

==>f=4.5

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