One of my homework problems deals with finding the change in entropy of the surroundings using the equation
delta(S)= -delta(H)/T(temp.)
The numbers given were T=263K and delta(H)fusion=6.0*10^(3) J/mol
I know how to solve the problem, I just want to know why it is that even though the answer I got was negative, "it must be positive because of the surroundings." I was hoping someone would explain the concept behind this just so I understand. Thanks!
You didn't post all of the problem so this is the best guess I can come up with but I assume it is because delta H for the process in question is negative which makes -dH/T positive.
Entropy is a measure of the randomness or disorder of a system. In the equation delta(S) = -delta(H)/T, delta(S) represents the change in entropy, delta(H) represents the change in enthalpy, and T represents the temperature.
The negative sign in front of delta(H) indicates that the change in enthalpy is released or given off by the system to the surroundings. This means that the surroundings gain energy from the system. Since enthalpy has the same sign as energy, a decrease in enthalpy in the system corresponds to an increase in energy for the surroundings.
When we consider entropy, it represents the distribution or spreading out of energy. In this case, when the system releases energy, it increases the randomness or disorder of the surroundings. This increase in randomness results in a positive change in entropy for the surroundings.
In other words, the negative change in enthalpy (delta(H)) corresponds to a positive change in entropy (delta(S)) for the surroundings because the release of energy by the system increases the randomness of the surroundings.