# The Entropy Change of Melting Ice: Why is the Equation Written as ΔS = Q/T?

• ChiralSuperfields
In summary, the conversation discusses the use of symbols to represent heat transfer in the change of entropy equation. It is suggested that using the symbol ##\Delta Q## can be misleading as heat is a transfer variable and not a state variable. Instead, it is recommended to use the symbol ##Q## or ##W## to represent heat and work, respectively, in a process. The analogy is made that just as ##\Delta W## should not be interpreted as a change in work, ##\Delta Q## should not be interpreted as a change in heat.
ChiralSuperfields
Homework Statement
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Why dose they write the change in entropy equation as ##\Delta S = \frac{Q}{T}##? Would it not better to write it as ##\Delta S = \frac{\Delta Q}{T}##, since it clear that we are only concerned about the transfer of heat in our system while it remains at constant temperature as all the energy goes into the change in phase.

Many thanks!

Callumnc1 said:

For this,
View attachment 324174

Why dose they write the change in entropy equation as ##\Delta S = \frac{Q}{T}##? Would it not better to write it as ##\Delta S = \frac{\Delta Q}{T}##, since it clear that we are only concerned about the transfer of heat in our system while it remains at constant temperature as all the energy goes into the change in phase.

Many thanks!
You are thinking correctly. However, ##Q## is often used for the heat transferred in a process. The symbol ##\Delta Q## for the heat transferred is also sometimes used. But, this symbol can be misleading if ##\Delta Q## is interpreted as "the change in ##Q##", or as ##\Delta Q = Q_f - Q_i##. The symbols ##Q_f## and ##Q_i## do not have any meaning. The initial and final states of the system do not "have heat". In more formal words, "heat is not a state variable".

ChiralSuperfields
TSny said:
You are thinking correctly. However, ##Q## is often used for the heat transferred in a process. The symbol ##\Delta Q## for the heat transferred is also sometimes used. But, this symbol can be misleading if ##\Delta Q## is interpreted as "the change in ##Q##", or as ##\Delta Q = Q_f - Q_i##. The symbols ##Q_f## and ##Q_i## do not have any meaning. The initial and final states of the system do not "have heat". In more formal words, "heat is not a state variable".
Thank you for your reply @TSny! Oh I think I see what you mean. Since heat is a 'transfer variable', it inherently describing a transition between the of energy between the finial and previous state.

Callumnc1 said:
Thank you for your reply @TSny! Oh I think I see what you mean. Since heat is a 'transfer variable', it inherently describing a transition between the of energy between the finial and previous state.
Yes. ##Q## is always associated with a process, and it refers to the energy transferred due to a temperature difference during the process. Likewise, work ##W## is always associated with a process. You might sometimes see ##\Delta W## for the work, but we would never think of this as ##\Delta W = W_f - W_i##.

ChiralSuperfields
TSny said:
Yes. ##Q## is always associated with a process, and it refers to the energy transferred due to a temperature difference during the process. Likewise, work ##W## is always associated with a process. You might sometimes see ##\Delta W## for the work, but we would never think of this as ##\Delta W = W_f - W_i##.
Ahh thank you very much @TSny! That is a very good analogy!

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