Help me please...! take home quiz >.<

A 1Kg of Water at 80 degree Celsius is added to 0.8Kg of water at 20 degree Celsius find the change in entropy.?

To find the change in entropy, we can use the formula:

ΔS = ∫(dq/T)

where ΔS is the change in entropy, dq is the heat transfer, and T is the temperature.

Now, let's break down the problem step by step:

1. Calculate the heat transfer between the two substances:
- For the 1kg of water at 80°C: q₁ = m₁ * c * ΔT
- For the 0.8kg of water at 20°C: q₂ = m₂ * c * ΔT
Here, m₁ and m₂ are the masses of the water, c is the specific heat capacity of water, and ΔT is the change in temperature.

2. Calculate the total heat transfer: q = q₁ + q₂

3. Since there is no heat transfer to the surroundings, the total heat transfer is zero: q = 0

4. Now we can use the formula for entropy change: ΔS = ∫(dq/T). Since q is zero, the integral becomes:
ΔS = ∫(0/T) = 0

Therefore, the change in entropy is zero, which means there is no change in the overall entropy of the system when the two substances are mixed.