Does Entropy Change Consider Irreversibility in Solids and Liquids?

In summary: Since ##T_1## is a constant for the reservoir, this is exactly equal to ##Q/T##. So the two equations are equivalent. In summary, the entropy change for a solid or liquid can be expressed as Cp(or Cv)ln(T2/T1) or Q/T(integral)+ Sgen. The first equation is correct, but the second equation may only be applicable if T represents the temperature at the boundary with the surroundings and the integration is over time. When considering the entropy change of a reservoir, it is typically expressed as Q/T instead of being zero, as the high heat capacity of the reservoir allows for a negligible change in temperature and thus a simplification of the equation. This is due to the fact
  • #1
son hong chang
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usually, entropy change in solid and liquid is formulated as Cp(or Cv)ln(T2/T1) or Q/T(integral)+ Sgen.
so, considering the former and the latter equations, Do their entropy changes include irreversibility due to Sgen?

And next question,
reservoir has no change in temperature and volume. therefore, its'entropy change is zero.
(According to this formula: dS=Cvln(T2/T1)+Rln(V2/V1) )
but when we solve many matters in thermodynamics especially in entropy part, we think that the reservoir exchanging the heat with another part has the entropy change expressed as Q/T not zero.
why is that?
 
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  • #2
Because the reservoir has infinite heat capacity?
(Just my guess that this confused you.)
 
  • #3
son hong chang said:
usually, entropy change in solid and liquid is formulated as Cp(or Cv)ln(T2/T1) or Q/T(integral)+ Sgen.
so, considering the former and the latter equations, Do their entropy changes include irreversibility due to Sgen?
The first equation is correct. I'm not sure about the second equation, unless T represents the temperature at the boundary with the surroundings and the integration is over time. The change in entropy from and initial thermodynamic equilibrium state to a final thermodynamic equilibrium state of a system depends only on the initial and final states, and not on the path between the two states.
And next question,
reservoir has no change in temperature and volume. therefore, its'entropy change is zero.
(According to this formula: dS=Cvln(T2/T1)+Rln(V2/V1) )
but when we solve many matters in thermodynamics especially in entropy part, we think that the reservoir exchanging the heat with another part has the entropy change expressed as Q/T not zero.
why is that?
The formula you wrote is for an ideal gas, which would not normally be used as a reservoir. But if you apply ##ΔS=mC_v\ln{(T_2/T_1)}## to a reservoir that has a very high value of ##mC_v##, you find that it reduces to Q/T. Here's how:

$$ΔS=mC_v\ln{(T_2/T_1)}=mC_v\ln{\left(1+\frac{(T_2-T_1)}{T_1}\right)}$$
If ##mC_v## is very large (as is the case of a reservoir, where it is infinite), the temperature change is very small. So we can expand the natural log term in a Taylor series and retain only the first term in the expansion. We thereby obtain:
$$ΔS\rightarrow mC_v\frac{(T_2-T_1)}{T_1}$$
But, $$mC_v(T_2-T_1)=Q$$Therefore,
$$ΔS\rightarrow \frac{Q}{T_1}$$
 
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1. What is entropy?

Entropy is a measure of the disorder or randomness in a system. It is a thermodynamic property that describes the distribution of energy within a system or between a system and its surroundings.

2. How is entropy related to solid and liquid states of matter?

Entropy increases as a substance moves from a solid to a liquid state. This is because the molecules in a solid are highly ordered and have less freedom to move, while in a liquid state the molecules have more freedom to move and are less ordered, resulting in a higher entropy.

3. Can entropy change be negative?

Yes, entropy change can be negative. This means that the disorder or randomness in a system has decreased, resulting in a decrease in entropy. This can happen when a substance moves from a more disordered state to a more ordered state, such as when a gas is compressed into a liquid.

4. What factors affect the entropy change of a substance?

The entropy change of a substance is affected by temperature, pressure, and the physical state of the substance. Generally, as temperature and pressure increase, the entropy also increases. The physical state also plays a role, with gases having higher entropy than liquids, and liquids having higher entropy than solids.

5. How is entropy change calculated?

The change in entropy of a substance can be calculated using the equation ΔS = Q/T, where ΔS is the change in entropy, Q is the heat energy transferred, and T is the temperature in Kelvin. This equation is based on the second law of thermodynamics, which states that the total entropy of a closed system will never decrease over time.

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