14. 100 g of water, H2O, is heated from 25C to 50C. What is the entropy change for
the process?
Cp = 4.2J/K·mol for water?
dS = 100 x 4.2 x ln(T2/T1)
Remember to use kelvin for T2 and T1.
To calculate the entropy change for the given process, we can use the formula:
ΔS = nCp ln(T2/T1)
where:
ΔS is the entropy change,
n is the number of moles,
Cp is the molar heat capacity,
T2 is the final temperature, and
T1 is the initial temperature.
First, let's find the number of moles of water using its molar mass. The molar mass of water (H2O) is approximately 18 g/mol. So, 100 g of water is equal to 100/18 = 5.56 mol.
Now, we have:
n = 5.56 mol,
Cp = 4.2 J/K·mol,
T1 = 25°C + 273.15 = 298.15 K (convert to Kelvin),
T2 = 50°C + 273.15 = 323.15 K (convert to Kelvin)
Substituting these values into the formula:
ΔS = (5.56 mol) * (4.2 J/K·mol) * ln(323.15 K / 298.15 K)
Now, you can use a calculator to evaluate this expression:
ΔS ≈ 10.46 J/K
Therefore, the entropy change for the process is approximately 10.46 J/K.