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 when two substances are mixed, we can use the formula:

ΔS = Sfinal - Sinitial

where ΔS is the change in entropy, Sfinal is the final entropy, and Sinitial is the initial entropy.

The entropy change for a substance can be calculated using the equation:

ΔS = m * c * ΔT

where ΔS is the change in entropy, m is the mass of the substance, c is the specific heat capacity, and ΔT is the change in temperature.

In this case, we have two substances: water at 0.0°C and water at 96.9°C. We need to calculate the entropy change for each substance and then find the net change by subtracting the initial entropy from the final entropy.

For water at 0.0°C, the initial entropy is zero because the substance is at its freezing point. We need to find the entropy change when it reaches the final temperature.

ΔS1 = m1 * c1 * ΔT1

Where:
m1 = mass of water at 0.0°C = 213 g
c1 = specific heat capacity of water = 4.18 J/g°C
ΔT1 = final temperature - initial temperature = 96.9°C - 0.0°C = 96.9°C

ΔS1 = 213 g * 4.18 J/g°C * 96.9°C

For water at 96.9°C, we need to find the entropy change when it cools down to the final temperature.

ΔS2 = m2 * c2 * ΔT2

Where:
m2 = mass of water at 96.9°C = 213 g
c2 = specific heat capacity of water = 4.18 J/g°C
ΔT2 = final temperature - initial temperature = 96.9°C - 0.0°C = 96.9°C

ΔS2 = 213 g * 4.18 J/g°C * (-96.9°C)

Once you have calculated ΔS1 and ΔS2, you can find the net change in entropy by subtracting the initial entropy from the final entropy.

ΔS = ΔS1 + ΔS2

Remember to convert the units, if necessary, to match the specific heat capacity values used in the equations.