Find the net change in entropy when 259 g of water at 0.0°C is added to 259 g of water at 97.5°C.
To find the net change in entropy, we first need to calculate the change in entropy for each sample of water and then sum them up.
The change in entropy for a substance can be calculated using the formula:
ΔS = mcΔT
Where:
ΔS is the change in entropy
m is the mass of the substance
c is the specific heat capacity of the substance
ΔT is the change in temperature
Let's calculate the change in entropy for each sample of water:
For the water at 0.0°C:
We know the mass of water is 259 g and the specific heat capacity of water is 4.184 J/g°C.
ΔT = final temperature - initial temperature
ΔT = 97.5°C - 0.0°C
ΔT = 97.5°C
ΔS = (259 g) * (4.184 J/g°C) * (97.5°C)
ΔS = 104,479.62 J/°C
For the water at 97.5°C:
The calculation is the same, but the initial temperature is now 97.5°C and the final temperature is 0.0°C.
ΔT = final temperature - initial temperature
ΔT = 0.0°C - 97.5°C
ΔT = -97.5°C
ΔS = (259 g) * (4.184 J/g°C) * (-97.5°C)
ΔS = -104,479.62 J/°C
Now, we can find the net change in entropy by summing up the individual changes in entropy:
Net change in entropy = ΔS (water at 0.0°C) + ΔS (water at 97.5°C)
Net change in entropy = 104,479.62 J/°C + (-104,479.62 J/°C)
Net change in entropy = 0 J/°C
Therefore, the net change in entropy when 259 g of water at 0.0°C is added to 259 g of water at 97.5°C is 0 J/°C.