Question

Calculate the change in entropy of 3 moles of liquid water if you heat it from 5˚C to 95˚C. The molar heat capacity of liquid water is 75.38 J/molK. Please report your answer one point past the decimal with the unit J/K.

Answer 1

Answer: The entropy change of the liquid water is 63.4 J/K

Explanation:

To calculate the entropy change for same phase at different temperature, we use the equation:

$\Delta S=n\times C_{p}\times \ln (\frac{T_2}{T_1})$

where,

$\Delta S$ = Entropy change

$C_{p}$ = molar heat capacity of liquid water = 75.38 J/mol.K

n = number of moles of liquid water = 3 moles

$T_2$ = final temperature = $95^oC=[95+273]K=368K$

$T_1$ = initial temperature = $5^oC=[5+273]K=278K$

Putting values in above equation, we get:

$\Delta S=3mol\times 75.38J/mol.K\times \ln (\frac{368}{278})\\\\\Delta S=63.4J/K$

Hence, the entropy change of the liquid water is 63.4 J/K