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Chapter 1: Q.1.43 (page 31)

Calculate the heat capacity of liquid water per molecule, in terms of K . Suppose (incorrectly) that all the thermal energy of water is stored in quadratic degrees of freedom. How many degrees of freedom would each molecule have to have?

Short Answer

Expert verified

Short Answer :

Heat capacity per molecule Cm=9.072k

Degrees of freedom f = 18

Step by step solution

01

Given Information :

Water's thermal energy is stored in quadratic degrees of freedom

02

Explanation 

The specific heat capacity of water is cwater=1cal路g-1路C-1=4.186J-1g-1路C-1, and the molar weight of water is 18.015g路mol -1so in 1gramof water.

N=Number of molecules in one moleMass of one mole=6.022脳102318.015

N=3.343脳1022molecules

The heat capacity of a single molecule is therefore:

Cm=CN=4.1863.343脳1022=1.252脳10-22J路C-1Cm=1.252脳10-22脳kk=1.252脳10-22脳k1.38脳10-23Cm=9.072k

03

Explanation

The heat capacity is linearly proportional to the number of degrees of freedom, according to the equipartition theorem,

Cm=fk2

Therefore now on comparing heat capacities, we have

fk2=9.072k

f=18

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