Final answer:
The change in entropy of water when heated from 20°C to 100°C can be calculated using the formulas ΔS = (Q / T) and Q = mcΔT. By substituting the values, the change in entropy is found to be 179.1 J/K.
Step-by-step explanation:
The change in entropy of water can be calculated using the formula:
ΔS = (Q / T)
Where ΔS is the change in entropy, Q is the heat added to the system, and T is the temperature in Kelvin.
In this case, the heat added to the water is calculated using the formula:
Q = mcΔT
Where m is the mass of the water, c is the specific heat capacity of water, and ΔT is the change in temperature.
Given that the mass of the water is 50 grams, the specific heat capacity of water is 4.18 J/g°C, and the change in temperature is 80°C, we can calculate Q. Substituting the values into the equation, we get:
Q = (50 g) * (4.18 J/g°C) * (80°C) = 16720 J
Now, by substituting the values into the first equation, we can calculate the change in entropy:
ΔS = (16720 J) / (100°C - 20°C + 273.15 K) = 179.1 J/K
Therefore, the change in entropy of the water in this process is 179.1 J/K.