Find the net change in entropy when 213 g of water at 0.0°C is added to 213 g of water at 96.9°C.

To find the net change in entropy, we need to calculate the change in entropy for each part of the process and then add them together.

First, let's calculate the change in entropy when the 213 g of water at 0.0°C is heated to 96.9°C. We can use the equation:

ΔS = m × Cp × ln(T2/T1)

Where:
ΔS = change in entropy
m = mass of the substance (in this case, water) = 213 g
Cp = specific heat capacity of water = 4.18 J/g°C
T1 = initial temperature = 0.0°C
T2 = final temperature = 96.9°C

Plugging in these values, we get:

ΔS1 = 213 g × 4.18 J/g°C × ln(96.9/0.0)

Next, let's calculate the change in entropy when the two masses of water at different temperatures are mixed. We can use the equation:

ΔS = m × Cp × ln(Tf/Ti)

Where:
ΔS = change in entropy
m = total mass of the combined water = 213 g + 213 g = 426 g
Cp = specific heat capacity of water = 4.18 J/g°C
Ti = initial temperature of the mixture (in this case, 96.9°C)
Tf = final temperature of the mixture (in this case, the equilibrium temperature)

Since the two masses of water have equal masses and initially equal temperatures, the final temperature of the mixture will be the average of the initial temperatures. Thus:

Tf = (0.0°C + 96.9°C) / 2 = 48.45°C

Plugging in these values, we get:

ΔS2 = 426 g × 4.18 J/g°C × ln(48.45/96.9)

Finally, we can find the net change in entropy by adding ΔS1 and ΔS2 together:

net ΔS = ΔS1 + ΔS2

Simply insert the values calculated above for ΔS1 and ΔS2 into the equation to find the net change in entropy.